1.6 notes
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The document defines and classifies different types of polygons. It begins by defining a polygon as a closed figure formed by three or more line segments that intersect only at their endpoints. Polygons are then classified based on their number of sides, such as triangles having 3 sides, quadrilaterals having 4 sides, and pentagons having 5 sides. Additional classifications include whether the polygon is convex or concave as well as whether it is equilateral, equiangular, or regular. Homework problems on classifying polygons are assigned at the end.
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The document provides an agenda and lesson notes for a geometry class. It includes definitions for distance, equidistant, and perpendicular bisector. It then states two theorems: 1) If two points are each equidistant from the endpoints of a segment, then the two points determine the perpendicular bisector of that segment. 2) If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of that segment. Examples are given to prove statements about equidistance and perpendicular bisectors. The exit slip asks students to identify two points equidistant from points A and B using an auxiliary line, and homework problems are assigned.
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This document provides a lesson plan on classifying triangles by their angles and side lengths. It begins with activating prior knowledge of angle types and having students draw and define acute, obtuse, right and straight angles. It then defines and provides examples of acute, obtuse, right, scalene, isosceles and equilateral triangles. Students are asked to classify sample triangles and solve problems identifying triangle types. The document concludes with a partner activity to create and classify triangles.
8.1 notes
The document discusses polygons and their interior and exterior angles. It states that the sum of the interior angles of any polygon is (n-2)180 degrees, where n is the number of sides. It also notes that the sum of the interior angles of any quadrilateral is always 360 degrees. Additionally, the sum of the exterior angles of any polygon is also 360 degrees.
5.3 5.4 notes
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.
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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This document discusses geometric probability and provides examples of calculating probabilities based on ratios of lengths and areas. It gives the example of calculating the probability that a driver will be pulled over in front of a school based on the length of road in front of the school compared to the total length of the road. Another example calculates the probability that a fly will land on a beach ball based on the area of the beach ball relative to the total area of a blanket. The document concludes with assigning homework problems from page 774 #4-10 evens, 20-23, 30-33.
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This document defines congruent figures as those where all corresponding parts are equal in measure. It introduces the Third Angle Theorem, which states that if two angles in one triangle are equal to two angles in another triangle, then the third angles are also equal. It also presents Theorem 4.4 on the properties of congruent triangles: reflexive, symmetric, and transitive properties. Homework problems are assigned.
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The document provides an agenda and lesson notes for a geometry class. It includes definitions for distance, equidistant, and perpendicular bisector. It then states two theorems: 1) If two points are each equidistant from the endpoints of a segment, then the two points determine the perpendicular bisector of that segment. 2) If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of that segment. Examples are given to prove statements about equidistance and perpendicular bisectors. The exit slip asks students to identify two points equidistant from points A and B using an auxiliary line, and homework problems are assigned.
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This document provides a lesson plan on classifying triangles by their angles and side lengths. It begins with activating prior knowledge of angle types and having students draw and define acute, obtuse, right and straight angles. It then defines and provides examples of acute, obtuse, right, scalene, isosceles and equilateral triangles. Students are asked to classify sample triangles and solve problems identifying triangle types. The document concludes with a partner activity to create and classify triangles.
8.1 notes
The document discusses polygons and their interior and exterior angles. It states that the sum of the interior angles of any polygon is (n-2)180 degrees, where n is the number of sides. It also notes that the sum of the interior angles of any quadrilateral is always 360 degrees. Additionally, the sum of the exterior angles of any polygon is also 360 degrees.
5.3 5.4 notes
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.
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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This document discusses geometric probability and provides examples of calculating probabilities based on ratios of lengths and areas. It gives the example of calculating the probability that a driver will be pulled over in front of a school based on the length of road in front of the school compared to the total length of the road. Another example calculates the probability that a fly will land on a beach ball based on the area of the beach ball relative to the total area of a blanket. The document concludes with assigning homework problems from page 774 #4-10 evens, 20-23, 30-33.
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This document defines congruent figures as those where all corresponding parts are equal in measure. It introduces the Third Angle Theorem, which states that if two angles in one triangle are equal to two angles in another triangle, then the third angles are also equal. It also presents Theorem 4.4 on the properties of congruent triangles: reflexive, symmetric, and transitive properties. Homework problems are assigned.
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1) The document discusses parallel lines and transversals. It defines the corresponding angles postulate, the alternate interior angles theorem, and the alternate exterior angles theorem.
2) These state that if two parallel lines are cut by a transversal, then the corresponding angles are congruent, the alternate interior angles are congruent, and the alternate exterior angles are congruent.
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This document appears to be notes from a math class on identifying quadrilaterals. It includes examples of solving problems about the measures of angles and lengths of sides in different quadrilaterals. The class was split into groups to fill in properties of different quadrilaterals like rectangles, rhombi, squares, kites and trapezoids from their textbook. The document ends by listing the homework assignment.
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This document covers key concepts about segments and congruence in geometry. It defines segments as parts of lines between two points and introduces the ruler postulate for assigning coordinates to points. The segment addition postulate states that if a point B lies between points A and C, then the sum of segments AB and BC equals segment AC. It also defines congruent segments as those with the same length and provides examples of finding lengths using the segment addition postulate and determining congruence. Homework problems at the end reinforce these concepts.
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The document summarizes key properties of triangles, including:
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2) The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.
3) The acute angles of a right triangle are complementary, meaning their measures sum to 90 degrees.
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The document discusses properties of parallelograms. It states that a parallelogram is a quadrilateral with both pairs of opposite sides parallel. It presents several theorems: if a quadrilateral is a parallelogram, then its opposite sides are congruent; its opposite angles are congruent; its consecutive angles are supplementary, summing to 180 degrees; and its diagonals bisect each other. The document appears to be notes from a geometry class discussing key properties and theorems related to parallelograms.
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The document discusses two theorems for proving triangles are congruent:
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The document defines and provides examples of different types of symmetry:
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2) The lesson defined congruent figures as those where all pairs of corresponding parts are congruent, and taught students to identify corresponding parts of congruent triangles and polygons.
3) Students practiced applying the definition of congruence and the reflexive property to solve sample problems identifying congruent figures.
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2) The class agenda includes a lesson on defining congruent figures, identifying corresponding parts, and using the reflexive property.
3) Students are assigned homework problems identifying whether figures are congruent based on corresponding parts.
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The document defines and discusses properties of polygons, including:
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1) The document discusses parallel lines and transversals. It defines the corresponding angles postulate, the alternate interior angles theorem, and the alternate exterior angles theorem.
2) These state that if two parallel lines are cut by a transversal, then the corresponding angles are congruent, the alternate interior angles are congruent, and the alternate exterior angles are congruent.
3) It also presents the consecutive interior angles theorem, which states that if two parallel lines are cut by a transversal, then the sum of any pair of consecutive interior angles is 180 degrees.
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This document appears to be notes from a math class on identifying quadrilaterals. It includes examples of solving problems about the measures of angles and lengths of sides in different quadrilaterals. The class was split into groups to fill in properties of different quadrilaterals like rectangles, rhombi, squares, kites and trapezoids from their textbook. The document ends by listing the homework assignment.
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This document outlines the course description, rationale, materials, communication methods, expectations, and grading scale for Mrs. Hedrick's 2011-2012 Pre-Algebra class. The course will review basic math operations and introduce concepts covered in Algebra I using a Prentice Hall textbook. Students will be expected to follow rules, complete bellwork and homework, and take quizzes, tests, and projects to assess their learning. Grades will be calculated based on points earned in various categories.
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This document covers key concepts about segments and congruence in geometry. It defines segments as parts of lines between two points and introduces the ruler postulate for assigning coordinates to points. The segment addition postulate states that if a point B lies between points A and C, then the sum of segments AB and BC equals segment AC. It also defines congruent segments as those with the same length and provides examples of finding lengths using the segment addition postulate and determining congruence. Homework problems at the end reinforce these concepts.
4.1 notes
The document summarizes key properties of triangles, including:
1) The sum of the measures of the interior angles of any triangle is always 180 degrees.
2) The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.
3) The acute angles of a right triangle are complementary, meaning their measures sum to 90 degrees.
8.2 notes
The document discusses properties of parallelograms. It states that a parallelogram is a quadrilateral with both pairs of opposite sides parallel. It presents several theorems: if a quadrilateral is a parallelogram, then its opposite sides are congruent; its opposite angles are congruent; its consecutive angles are supplementary, summing to 180 degrees; and its diagonals bisect each other. The document appears to be notes from a geometry class discussing key properties and theorems related to parallelograms.
4.4 notes
The document discusses two theorems for proving triangles are congruent:
1) Side-Angle-Side (SAS) theorem - If two triangles have two sides and the included angle of one equal to two sides and the included angle of the other, then the triangles are congruent.
2) Hypotenuse-Leg (HL) theorem - If two right triangles have one hypotenuse and one leg of one equal to the hypotenuse and corresponding leg of the other, then the triangles are congruent. The document also notes that the Side-Side-Angle (SSA) relationship is not sufficient alone to prove triangles congruent.
9.6 notes
The document defines and provides examples of different types of symmetry:
1) A line of symmetry is a line where a figure can be mapped onto itself by a reflection.
2) Rotational symmetry occurs when a figure can be mapped onto itself by a rotation of 180 degrees or less.
3) A center of symmetry is the center point of a figure that displays symmetry.
4) Point symmetry is when every part of a figure has a matching part.
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The document discusses algebraic properties of equality that can be used for proofs, including:
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The document discusses measures of angles in polygons. It states the Polygon Interior Angles Theorem, which is that the sum of the interior angles of an n-sided polygon is (n-2)180 degrees. It also notes that the sum of the interior angles of a quadrilateral is 360 degrees. Additionally, it provides the Polygon Exterior Angles Theorem that the sum of the exterior angles of any polygon is 360 degrees.
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The document is from a geometry class and discusses classifying polygons. It defines polygons as closed figures with 3 or more sides where each side intersects exactly 2 other sides. Polygons are named by listing the vertices in order. They can be convex, with no interior points, or concave, with interior points. Common polygons include triangles, quadrilaterals, pentagons, and hexagons. Regular polygons are convex, equilateral, and equiangular. Students are assigned homework problems classifying polygons.
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The document defines and provides examples of several angle pair relationships:
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The document defines and discusses properties of polygons, including:
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The document is notes from a geometry class that:
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2) Lists the agenda for the class which includes turning in homework, discussing homework questions, learning about theorem 3-7, having an exit slip activity, and partner discussion.
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The document discusses properties of triangles and their angles. It begins with an activity where students cut out and label triangles to discover properties about the sum of interior angles and relationships between interior and exterior angles. The main points covered are:
- The sum of the measures of the interior angles of any triangle is 180 degrees.
- The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.
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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.
2015 Branson Tournament Schedule
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.
12.7 notes
This document contains notes from a math class on similar solids. It defines similar solids as two solids of the same type that have equal ratios, known as a scale factor. It then states the Similar Solids Theorem: if two similar solids have a scale factor of a:b, their corresponding areas have a ratio of a2:b2 and their corresponding volumes have a ratio of a3:b3. Examples of homework problems involving similar solids are listed.
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.
12.5 notes
The document is notes from a math class lesson on finding the volumes of cones and pyramids. It includes the objectives of learning the formulas for these volumes. The formulas given are that the volume of a cone is 1/3πr^2h and the volume of a pyramid is 1/3Bh, where B is the area of the base and h is the height. There are examples provided of applying these formulas to find volumes.
12.4 notes
This document contains notes from a math lesson on finding the volumes of prisms and cylinders. It defines volume as the amount of space inside an object. It explains that to find the volume of a prism or cylinder, you calculate the area of the base and multiply it by the height. For a prism, the base can be any shape and its area formula is used. For a cylinder, the base is a circle so the volume formula is πr^2h, with r as the radius and h as the height. Examples of volume problems are shown and homework problems are assigned from the textbook.
Indian volleyball tournament
A volleyball tournament will be held on May 2nd at 9am at the Max Evans Gym to benefit the Strafford Indian Volleyball Program. The tournament will feature fun rules, games and prizes and cost $10 per person to register, either as part of a team of 6-8 players or individually. People can register their teams on Facebook or by contacting the coaches Ashley Bough or Angelina Hedrick by May 1st.
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
This document contains information about the law of sines for a math homework assignment. It lists the topic as the law of sines and directs the student to problems 15-17 and 29-31 on page 672 of their homework, which was assigned on April 08, 2015. The document repeats this information four times.
12.1 notes
This document contains notes from a math class where students were working on homework problems involving trigonometry (SOHCAHTOA) and multiples of 3. The notes are dated April 08, 2015 and reference homework page 648 problems 12 through 36 dealing with multiples of 3.
11.7 notes
This document contains notes from an 11th grade math class on the topic of geometric probability. It includes examples of calculating the probability of events based on ratios of lengths and areas, such as the probability of a driver speeding in front of a school based on the length of road in front of the school over the total road length. The homework problems assigned were problems 4-10 of the even numbers, 20-23, and 30-33 on page 774 of the textbook.
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1.6 notes
- 1. 1.6 Classify Polygons August 22, 2011 Bellwork 1. What are complementary angles? sum = 90 degrees 2. m JLM? M 105 15 L 105 + 15 = 120 J 3. Given that 3 is a supplement of 4 and m 3=119 , find m 4. 4. Name a pair of vertical angles. 180 119 = 61 2 1 1,4; 2,5; 3,6 3 6 4 5 5. Did you know that you may use your notes on Bellwork? Yes you may! HW pg. 44 #329 odds 1
- 2. 1.6 Classify Polygons August 22, 2011 1.6 Classify Polygons Polygon: closed figure w/ 1. formed by 3 or more sides 2. each side intersects exactly 2 sides at each endpoint (no collinear points) Naming a polygon: list the vertices in consecutive order A B D Vertex C E Identifying a polygon: Convex: no line contains Concave: a line contains a a point in the interior vs. point in the interior of of the polygon the polygon. HW pg. 44 #329 odds 2
- 3. 1.6 Classify Polygons August 22, 2011 HW pg. 44 #329 odds 3
- 4. 1.6 Classify Polygons August 22, 2011 Classifying Polygons 3 4 5 6 10 Triangle Quadrilateral Pentagon Hexagon Decagon ngon: n is the number of sides Equilateral: all sides ≅ Equiangular: all angles in interior are ≅ Regular: covex, equilateral & equiangular HW pg. 44 #329 odds 4
- 5. 1.6 Classify Polygons August 22, 2011 HW pg. 44 #329 odds 5
- 6. 1.6 Classify Polygons August 22, 2011 HW pg. 44 #329 odds 6
- 7. 1.6 Classify Polygons August 22, 2011 HW pg. 44 #329 odds 7
- 8. 1.6 Classify Polygons August 22, 2011 HW: pg. 44 #329 odds HW pg. 44 #329 odds 8