5.3 5.4 notes
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The document discusses theorems and properties related to angle bisectors, medians, and altitudes of triangles. It provides definitions of an angle bisector, median, altitude, and centroid. It states the Angle Bisector Theorem, Converse of the Angle Bisector Theorem, Concurrency of Medians of a Triangle Theorem, and Concurrency of Altitudes Theorem. The document assigns math problems from sections 5.1, 5.2, 5.3, and 5.4 and lists bellwork tasks.
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5.1 5.2 notes
This document discusses midsegments and perpendicular bisectors of triangles. It defines a midsegment as a segment connecting the midpoints of two sides of a triangle, and states that every triangle has three midsegments that are parallel to the opposite side and half as long. It also defines a perpendicular bisector as a line perpendicular to a segment at its midpoint, and explains that all points on the bisector are equidistant from the endpoints. Additionally, it introduces the circumcenter as the point where the three perpendicular bisectors of a triangle intersect.
1
The document defines key geometric terms like included side, included angle, and postulates. It then describes several postulates for proving triangle congruence: the SSS postulate states that if three sides of one triangle are equal to three sides of another, the triangles are congruent. The SAS postulate states that if two sides and the included angle of one triangle are equal to those of another, the triangles are congruent. The ASA and SAA postulates similarly define relationships between angles and sides that prove triangle congruence.
Geom 3point1and2
The document discusses relationships between lines and angles formed by transversals. It defines parallel lines as lines that do not intersect and are coplanar, and skew lines as lines that do not intersect and are not coplanar. A transversal is a line that intersects two or more coplanar lines. When a transversal crosses lines, it forms corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles that have specific relationships. Perpendicular lines intersect to form four right angles.
Geo 4.2 3-notes_cong_triangles
The document discusses four postulates and theorems for determining if two triangles are congruent: the Side-Side-Side postulate, the Side-Angle-Side postulate, the Angle-Side-Angle postulate, and the Angle-Angle-Side theorem. These state that if corresponding sides or angles of two triangles are congruent in certain combinations, then the two triangles are congruent. Homework assigned is to complete problems #25 from the 4.2 and 4.3 worksheet.
1.5 terms
This document defines key geometry terms related to dividing segments and angles. It defines a midpoint as the point on a segment that divides it into two equal parts. A segment bisector achieves the same division of a segment and contains the midpoint. An angle bisector divides an angle into two congruent angles. The midpoint formula is provided to find the midpoint between two points on a coordinate plane by averaging their x and y values.
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The document discusses various bisectors and segments related to triangles, including:
- The perpendicular bisectors and angle bisectors of a triangle are concurrent, intersecting at the circumcenter and incenter respectively.
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- Key properties are discussed, such as the circumcenter theorem relating the circumcenter to triangle vertices, and the incenter theorem relating the incenter to triangle sides.
Geom 5point1and2
This document discusses perpendicular bisectors and angle bisectors of triangles. It defines perpendicular and angle bisectors and explains their properties. The key points are:
1) The perpendicular bisectors of a triangle are concurrent lines that intersect at a single point equidistant from the triangle's vertices, called the circumcenter.
2) The angle bisectors of a triangle are also concurrent lines intersecting at a single point equidistant from the triangle's sides, called the incenter.
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This document contains a series of true/false and multiple choice questions about geometry concepts such as if-then statements, angle relationships, perpendicular lines, congruent angles, midpoints, and properties used in proofs. The questions cover conditional and biconditional statements, angle pairs such as complementary and supplementary angles, theorems about perpendicular lines and midpoints, and valid reasons used in geometric proofs.
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5.1 5.2 notes
This document discusses midsegments and perpendicular bisectors of triangles. It defines a midsegment as a segment connecting the midpoints of two sides of a triangle, and states that every triangle has three midsegments that are parallel to the opposite side and half as long. It also defines a perpendicular bisector as a line perpendicular to a segment at its midpoint, and explains that all points on the bisector are equidistant from the endpoints. Additionally, it introduces the circumcenter as the point where the three perpendicular bisectors of a triangle intersect.
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The document defines key geometric terms like included side, included angle, and postulates. It then describes several postulates for proving triangle congruence: the SSS postulate states that if three sides of one triangle are equal to three sides of another, the triangles are congruent. The SAS postulate states that if two sides and the included angle of one triangle are equal to those of another, the triangles are congruent. The ASA and SAA postulates similarly define relationships between angles and sides that prove triangle congruence.
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Geo 4.2 3-notes_cong_triangles
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1.5 terms
This document defines key geometry terms related to dividing segments and angles. It defines a midpoint as the point on a segment that divides it into two equal parts. A segment bisector achieves the same division of a segment and contains the midpoint. An angle bisector divides an angle into two congruent angles. The midpoint formula is provided to find the midpoint between two points on a coordinate plane by averaging their x and y values.
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The document discusses various bisectors and segments related to triangles, including:
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This document discusses perpendicular bisectors and angle bisectors of triangles. It defines perpendicular and angle bisectors and explains their properties. The key points are:
1) The perpendicular bisectors of a triangle are concurrent lines that intersect at a single point equidistant from the triangle's vertices, called the circumcenter.
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This PowerPoint presentation introduces different criteria for determining if two triangles are congruent: 1) If three sides of one triangle are equal to three sides of another triangle. 2) If two sides and the included angle of one triangle are equal to those of another triangle. 3) If one side and the two angles adjacent to it of one triangle are equal to those of another triangle. 4) If three angles of one triangle are equal to three angles of another triangle. The document provides examples to illustrate each of the criteria for congruent triangles.
Proving lines are parallel
The document discusses several theorems and properties for proving when two lines are parallel, including:
1) If corresponding angles formed by a transversal intersecting two lines are congruent, then the lines are parallel.
2) If alternate interior angles or alternate exterior angles formed by a transversal are congruent, then the lines are parallel.
3) If consecutive interior angles formed by a transversal are supplementary, then the lines are parallel.
It also provides an example of using these properties to prove that if two boats sail at 45 degree angles to the constant wind, their paths will not cross since their paths are parallel.
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- A transversal is a line that intersects two or more lines.
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Lesson2 unit-10 (2)
Here are the solutions to the word problems:
1. Since the radius bisects chord AB at midpoint Q, AQ and QB would each be 2 inches based on the definition of bisect.
2. Since the radius OA passes through chord BC at its midpoint D, radius OA must be perpendicular to chord BC based on the Bisected Chord Theorem.
3. If chord SB has an apothem of 2 inches and arc measure of 75°, and SB is congruent to CE, then the apothem of CE must also be 2 inches and the arc measure of CE must also be 75° based on the Congruent Chords Theorem.
Geom 4point3
This document discusses two methods for proving triangles are congruent: the Side-Side-Side (SSS) method and the Side-Angle-Side (SAS) method. SSS states that if all three sides of one triangle are congruent to another triangle, then the triangles are congruent. SAS states that if two sides and the included angle of one triangle are congruent to those of another triangle, then the triangles are congruent. Examples are provided to demonstrate how to use SSS and SAS to prove triangle congruence.
Example Ratios
The lengths of line segments AB and BD are in a 2:3 ratio. The length of line segment AD is given as 20. By setting AB = 2x and BD = 3x, where x is the common factor, and using the equation AD = AB + BD, the value of x is found to be 4. Therefore, the lengths of AB and BD are 8 and 12 respectively.
Parallel Lines
This document discusses properties of parallel lines cut by a transversal. It defines key terms like parallel lines, transversal, corresponding angles, alternate interior angles, and alternate exterior angles. It then presents conjectures that corresponding angles, alternate interior angles, and alternate exterior angles are congruent when two parallel lines are cut by a transversal. Examples are given to illustrate these properties and how determining the measure of one angle allows calculating the measures of all other angles formed.
Self learning material maths
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3.3 terms
This document outlines five theorems related to parallel lines cut by a transversal: 1) the corresponding angles postulate states corresponding angles are congruent, 2) the alternate interior angles theorem states alternate interior angles are congruent, 3) the consecutive interior angles theorem states consecutive interior angles are supplementary, 4) the alternate exterior angles theorem states alternate exterior angles are congruent, and 5) the perpendicular transversal theorem states if a transversal is perpendicular to one parallel line, it is perpendicular to the other.
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3-3 part 1 properties of parallel lines
This document discusses properties of parallel lines cut by a transversal. It introduces two postulates about corresponding angles being congruent if lines are parallel, and lines being parallel if corresponding angles are congruent. It then presents four theorems: if alternate interior angles or same-side interior angles of two lines cut by a transversal are congruent/supplementary, the lines are parallel; and if two lines are perpendicular to the same line, they are parallel. Finally, it lists five ways to prove two lines are parallel using the previous postulates and theorems.
Lesson2, unit 10
Here are the solutions to the word problems:
1. Since the radius bisects chord AB at midpoint Q, AQ and QB would each be 2 inches based on the definition of bisect.
2. Since the radius OA passes through chord BC at its midpoint D, radius OA must be perpendicular to chord BC based on the Bisected Chord Theorem.
3. If chord SB has an apothem of 2 inches and arc measure of 75°, and SB is congruent to CE, then the apothem of CE must also be 2 inches and the arc measure of CE must also be 75° based on the Congruent Chords Theorem.
9 7 perimeters and similarity
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4.6 notes
This document provides instructions to determine if pairs of triangles are congruent using several postulates: Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Side-Side-Side (SSS), Angle-Angle-Side (AAS), or Hypotenuse-Leg (HL). If congruence cannot be proven with one of these postulates, the response should be "not necessarily congruent". It then lists homework problems from page 259 numbers 4-16, 22, and 24 to practice applying these postulates.
8.1 notes
The document discusses angle measures in polygons. It defines a diagonal as a segment joining two non-consecutive vertices. The Polygon Interior Angles Theorem states that the sum of the interior angles of an n-sided polygon is (n-2)180. The Interior Angles of a Quadrilateral theorem says the sum of the interior angles is 360. The Polygon Exterior Angles Theorem states that the sum of the exterior angles is 360.
4.3 notes
This document discusses the Side-Side-Side (SSS) theorem for proving triangle congruence. It states that if three sides of one triangle are equal to the three sides of another triangle, then the triangles are congruent. The document provides an example of two triangles, ΔABC and ΔDEF, where the sides are labeled as equal. It also discusses using Angle-Angle-Angle (AAA) to show similarity, not congruence, of triangles. The homework assignment is problems #5-19 odd, 24, 26 on page 236.
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8.5 notes
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This PowerPoint presentation introduces different criteria for determining if two triangles are congruent: 1) If three sides of one triangle are equal to three sides of another triangle. 2) If two sides and the included angle of one triangle are equal to those of another triangle. 3) If one side and the two angles adjacent to it of one triangle are equal to those of another triangle. 4) If three angles of one triangle are equal to three angles of another triangle. The document provides examples to illustrate each of the criteria for congruent triangles.
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The document discusses several theorems and properties for proving when two lines are parallel, including:
1) If corresponding angles formed by a transversal intersecting two lines are congruent, then the lines are parallel.
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3) If consecutive interior angles formed by a transversal are supplementary, then the lines are parallel.
It also provides an example of using these properties to prove that if two boats sail at 45 degree angles to the constant wind, their paths will not cross since their paths are parallel.
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This document discusses parallel lines and transversals. It defines key terms like parallel lines, transversals, interior angles, exterior angles, corresponding angles, alternate interior angles, alternate exterior angles, same side interior angles, and same side exterior angles. The main points are:
- A transversal is a line that intersects two or more lines.
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This document discusses properties of parallel lines cut by a transversal. It states that if two parallel lines are cut by a transversal, then corresponding angles and alternate interior angles will be congruent. It also states that same-side interior angles will be supplementary. Finally, it notes that if a transversal is perpendicular to one of the parallel lines, then it is also perpendicular to the other parallel line.
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This document defines geometric concepts like congruent objects, segments, midpoints, and bisectors. It also introduces angles, describing them as dividing the plane into interior, exterior, and points on the angle. It discusses naming angles using different notation and measuring angles. Finally, it mentions classifying angles by their measures and the important Angle Addition Postulate.
Lesson2 unit-10 (2)
Here are the solutions to the word problems:
1. Since the radius bisects chord AB at midpoint Q, AQ and QB would each be 2 inches based on the definition of bisect.
2. Since the radius OA passes through chord BC at its midpoint D, radius OA must be perpendicular to chord BC based on the Bisected Chord Theorem.
3. If chord SB has an apothem of 2 inches and arc measure of 75°, and SB is congruent to CE, then the apothem of CE must also be 2 inches and the arc measure of CE must also be 75° based on the Congruent Chords Theorem.
Geom 4point3
This document discusses two methods for proving triangles are congruent: the Side-Side-Side (SSS) method and the Side-Angle-Side (SAS) method. SSS states that if all three sides of one triangle are congruent to another triangle, then the triangles are congruent. SAS states that if two sides and the included angle of one triangle are congruent to those of another triangle, then the triangles are congruent. Examples are provided to demonstrate how to use SSS and SAS to prove triangle congruence.
Example Ratios
The lengths of line segments AB and BD are in a 2:3 ratio. The length of line segment AD is given as 20. By setting AB = 2x and BD = 3x, where x is the common factor, and using the equation AD = AB + BD, the value of x is found to be 4. Therefore, the lengths of AB and BD are 8 and 12 respectively.
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This document discusses properties of parallel lines cut by a transversal. It defines key terms like parallel lines, transversal, corresponding angles, alternate interior angles, and alternate exterior angles. It then presents conjectures that corresponding angles, alternate interior angles, and alternate exterior angles are congruent when two parallel lines are cut by a transversal. Examples are given to illustrate these properties and how determining the measure of one angle allows calculating the measures of all other angles formed.
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This document outlines five theorems related to parallel lines cut by a transversal: 1) the corresponding angles postulate states corresponding angles are congruent, 2) the alternate interior angles theorem states alternate interior angles are congruent, 3) the consecutive interior angles theorem states consecutive interior angles are supplementary, 4) the alternate exterior angles theorem states alternate exterior angles are congruent, and 5) the perpendicular transversal theorem states if a transversal is perpendicular to one parallel line, it is perpendicular to the other.
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3-3 part 1 properties of parallel lines
This document discusses properties of parallel lines cut by a transversal. It introduces two postulates about corresponding angles being congruent if lines are parallel, and lines being parallel if corresponding angles are congruent. It then presents four theorems: if alternate interior angles or same-side interior angles of two lines cut by a transversal are congruent/supplementary, the lines are parallel; and if two lines are perpendicular to the same line, they are parallel. Finally, it lists five ways to prove two lines are parallel using the previous postulates and theorems.
Lesson2, unit 10
Here are the solutions to the word problems:
1. Since the radius bisects chord AB at midpoint Q, AQ and QB would each be 2 inches based on the definition of bisect.
2. Since the radius OA passes through chord BC at its midpoint D, radius OA must be perpendicular to chord BC based on the Bisected Chord Theorem.
3. If chord SB has an apothem of 2 inches and arc measure of 75°, and SB is congruent to CE, then the apothem of CE must also be 2 inches and the arc measure of CE must also be 75° based on the Congruent Chords Theorem.
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This document discusses perimeters and similarity of triangles. It introduces scale factors and explains that if two triangles are similar, then the ratios of their corresponding sides are equal and the ratios of their corresponding perimeters are proportional to the ratios of their corresponding sides. It provides examples of calculating scale factors between similar triangles and using scale factors to determine missing side lengths or perimeters. The document establishes that the ratio found by comparing measures of corresponding sides of similar triangles is called the constant of proportionality or scale factor.
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4.6 notes
This document provides instructions to determine if pairs of triangles are congruent using several postulates: Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Side-Side-Side (SSS), Angle-Angle-Side (AAS), or Hypotenuse-Leg (HL). If congruence cannot be proven with one of these postulates, the response should be "not necessarily congruent". It then lists homework problems from page 259 numbers 4-16, 22, and 24 to practice applying these postulates.
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5.3 5.4 notes
This document provides homework instructions and notes on geometry topics including:
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This document contains a geometry lesson on perpendicular bisectors and angle bisectors. It begins with definitions of perpendicular bisectors and angle bisectors. It then provides examples of using theorems about perpendicular bisectors and angle bisectors to find unknown measures in geometric figures. It also gives examples of writing equations of perpendicular bisectors and angle bisectors in the coordinate plane. The document aims to prove and apply theorems about perpendicular bisectors and angle bisectors.
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This document discusses various metric relationships in mathematics including proofs, congruency, similarity, angles, triangles, and the Pythagorean theorem. It defines key concepts such as complementary angles, supplementary angles, opposite angles, interior angles, corresponding angles, and more. Examples of exam questions are provided testing these concepts along with activities for further practice.
Chapter 5 day 3 with answers
1. The document is a geometry drill from December 17, 2013 that contains problems about triangle properties like perpendicular bisectors, angle bisectors, circumcenters, medians, altitudes, centroids, and orthocenters.
2. Key terms defined include median, centroid, altitude, and orthocenter of a triangle.
3. The document provides explanations of medians, altitudes, centroids, and orthocenters of triangles and their properties.
Module 1 similarity
This module introduces ratio, proportion, and the Basic Proportionality Theorem. Students will learn about ratios, proportions, and how to use the fundamental law of proportions to solve problems involving triangles. The module is designed to teach students to apply the definition of proportion of segments to find unknown lengths and illustrate and verify the Basic Proportionality Theorem and its Converse. Examples are provided to demonstrate how to express ratios in simplest form, find missing values in proportions, determine if ratios form proportions, and solve problems involving angles and segments in triangles using ratios and proportions.
Geometry unit 5.2
This document provides instruction on perpendicular and angle bisectors. It defines key terms such as equidistant, locus, and perpendicular bisector. It explains that an angle bisector is the locus of points equidistant from the sides of an angle. Examples are provided to demonstrate applying theorems about perpendicular and angle bisectors to find missing measures. Students are asked to construct perpendicular bisectors and angle bisectors, find midpoints and slopes, and solve problems involving perpendicular and angle bisectors.
Similarity.pdf
This document discusses concepts related to similarity and ratios in geometry. It defines scale factors and using ratios to solve for scaled values. It also describes the midpoint theorem, which states various properties relating midpoints and parallel lines. The intercept theorem is introduced as the principle that corresponding line segments cut by parallel lines are in the same ratio. Finally, it defines the golden ratio as a specific value where the ratio of two quantities equals the ratio of their sum to the larger quantity.
Coordinate geometry fundamentals 2012
This document provides information and instructions for performing coordinate geometry computations for surveying traverse loops. It defines key terms like azimuths, bearings, angles, and directions. It explains how to compute interior angles, azimuths, latitudes, and departures for traverse legs. It also describes how to balance a traverse loop by adjusting angles and applying corrections to latitudes and departures to minimize positional errors.
Geometry Section 5-1 1112
The document discusses bisectors of triangles, including perpendicular bisectors and angle bisectors. It defines key terms like perpendicular bisector, concurrent lines, circumcenter, and incenter. Theorems are presented about the properties of points on perpendicular bisectors, including that they are equidistant from the endpoints of the bisected segment. Similarly, points on angle bisectors are equidistant from the sides of the bisected angle. The circumcenter and incenter are shown to be equidistant from the vertices and sides of a triangle respectively. Examples demonstrate applying the concepts.
4.5 Special Segments in Triangles
* Construct perpendicular and angle bisectors
* Use bisectors to solve problems
* Identify the circumcenter and incenter of a triangle
* Use triangle segments to solve problems
Geometry Theorems.pdf
The document discusses two theorems:
1) The Midpoint Theorem, which states that if a line parallel to one side of a triangle cuts the other two sides, then it cuts them proportionally to the length of the sides. It also notes that the midpoint of a triangle's side bisects the opposite side.
2) The Intercept Theorem, which is a generalization of the Midpoint Theorem. It states that if two parallel lines are cut by two transversals, then the corresponding line segments are cut in the same ratio. It provides an example using a square divided into segments by its diagonals and midpoints of sides. Ratios of the areas of the resulting regions are calculated.
Obj. 21 Medians, Altitudes, and Midsegments
Identify altitudes and medians of triangles
Identify the orthocenter and centroid of a triangle
Use triangle segments to solve problems
Identify a midsegment of a triangle and use it to solve problems.
IIT JEE Coordinate Geometry- Preparation Tips to Practical Applications! - as...
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2.5.6 Perpendicular and Angle Bisectors
* Construct perpendicular and angle bisectors
* Use bisectors to solve problems
* Identify the circumcenter and incenter of a triangle
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IIT JEE Coordinate Geometry- Preparation Tips to Practical Applications! - as...
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This document outlines the Geometry 2016 Chapter 12 unit on 3D shapes that will be covered from April 11th to April 29th. It includes the chapter sections and topics to be covered each day, such as different types of prisms and pyramids, as well as the homework assignments and assessments including quizzes, tests, and a study guide.
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This document provides a schedule for Geometry Chapter 10 on Circles over a two week period from February 29th to March 11th and March 21st to March 25th. Each day covers a different section of the chapter, with assigned problems and quizzes listed. The schedule culminates with a paper plate review, studying for the chapter test, taking the test, and then correcting any errors on the test.
Ch 7 unit schedule
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The document summarizes a volleyball tournament taking place on October 3, 2015 in Stockton. It outlines the tournament structure, including three pools (A, B, C) divided by age/skill level with 4 teams each. A schedule is provided for round robin pool play matches between the teams, with the top two teams from each pool and the next two best records advancing to bracket playoff rounds. Bracket play will begin at 1:30 PM and be a best-of-three format to determine 1st, 2nd, and 3rd place trophies.
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The JV Lake Volley Fest 2015 volleyball tournament will take place on September 26th. Seven teams will be split into the Purple Pool and Gold Pool, with the top two teams from each pool advancing to the Championship Bracket and the bottom two advancing to the Consolation Bracket. The tournament schedule lists the matchups for each of the six time slots between 8:30am and 12:15pm across the two courts. Plaques will be awarded to the first and second place finishers.
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Camdenton High School will host the 2015 Lake Volley Fest Tournament on September 26th. There will be two courts located on campus for pool play and bracket play. Teams will be responsible for providing their own line judge. The top four teams will advance to the championship bracket, while the bottom four teams will play in the consolation bracket. Plaques will be awarded to the first and second place finishers.
Volleyfest Schedule 2015
This document contains the schedule for the 19th Annual Strafford Volleyfest volleyball tournament held on September 19, 2015. It lists the three courts where matches will take place and provides the schedule of games for each court, with start times ranging from 8:30 AM to 6:15 PM. It identifies the 12 participating schools that are divided into three pools based on color. It explains that after pool play, the top six teams will advance to the Championship Bracket and the bottom six to the Consolation Bracket for playoff matches.
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The document provides information about the 2015 Branson Invitational volleyball tournament including pool and bracket structures. Sixteen teams will be divided into four pools of four teams each to play a round robin. Pool play will consist of best-of-three sets and teams will be ranked 1-16 based on win-loss record, point differential, and head-to-head results. The top eight teams will advance to the gold bracket and bottom eight to the silver bracket for single elimination bracket play consisting of best-of-three sets.
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12.6 notes
The document discusses surface area and volume formulas for spheres. It provides examples of calculating the surface area of spheres with given diameters, as well as the volume of spheres and other objects like snow cones that can be modeled as spheres. Students are assigned homework problems applying these formulas to calculate surface areas and volumes.
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Indian volleyball tournament
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12.3 notes
This document contains notes and examples for calculating the surface area of pyramids and cones. It provides the formulas for finding the surface area of regular pyramids and cones. For pyramids, the surface area equals one-half the perimeter of the base times the sum of the slant height and apothem. For cones, the surface area equals pi times the radius squared plus pi times the radius times the slant height. The document includes practice problems applying these formulas to find the surface area of various pyramids and cones.
12.2 notes
The document discusses surface area formulas for prisms and cylinders. It defines surface area as the sum of the areas of all surfaces that enclose a solid. For prisms, surface area is calculated as the perimeter of the base multiplied by the height, plus twice the area of the base. For cylinders, surface area is the circumference of the base multiplied by the height, plus twice the area of the circular base. The document provides examples of applying these formulas to prisms and cylinders.
12.5 notes
This document contains information about the law of cosines from a geometry homework assignment on page 678 problems 14 through 20, dated April 09, 2015. The document title and date are repeated multiple times.
12.4 notes
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5.3 5.4 notes
- 1. Do problems on HW worksheet. 5.1 #2, 14 5.2 #2, 6, 8 5.1 2. x=8 14. DE = 17 5. 2 2. AB = 26 6. yes 8. DE = 44 Bellwork
- 2. 5.3 Angle Bisectors Angle Bisector Theorem: If a point is on the < bisector, then it is equidistant from the 2 sides of the angle. Conv erse of Angle Bisector Theorem: If a point is in the interior of an < and is equidistant from the sides of the <, then it lies on the < bisector. C B DB = DC AD bisects <BAC
- 3. 5.4 Medians & Altitudes Median: segment from a vertex to the midpoint of opposite side Centr oid: point of concurrency (intersection of medians) Co ncurrency of Medians of a Triangle Theorem: The medians intersect at a point that is 2/3 of the distance from each vertex to the midpoint of the opposite side. A C B P E F D AP = 2/3 AE BP = 2/3 BF CP = 2/3 CD
- 5. Altitude: perpendicular segment form a vertex to the opposite side Concu rrency of Altitudes Theorem: The lines containing the altitudes are concurrent.
- 6. HW 5 .3-5.4 Worksheet Evens