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The document discusses different postulates and theorems that can be used to prove triangles are congruent, including: 1) Angle-Side-Angle (ASA) - If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent. 2) Angle-Angle-Side (AAS or SAA) - If two angles and the non-included side of one triangle are equal to two angles and the non-included side of another triangle, then the triangles are congruent. 3) Angle-Angle-Angle (AAA) only proves triangles are similar, not congruent. Side-Side-Angle (SSA
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4.4 & 4.5 notes
The document discusses five triangle congruence theorems: side-angle-side (SAS), hypotenuse-leg (HL), angle-side-angle (ASA), angle-angle-side (AAS or SAA), and provides homework assignments involving applying these theorems. It notes that the side-side-angle (SSA) and angle-angle-angle (AAA) scenarios are not sufficient on their own to prove triangle congruence.
Geom 5.5 SSS and SAS
This document discusses different postulates and theorems for proving triangles congruent, including:
1. The Side-Side-Side (SSS) postulate, which states that if the three sides of one triangle are congruent to the three sides of another triangle, then the triangles are congruent.
2. The Side-Angle-Side (SAS) postulate, which states that if one angle and the two sides that form it in one triangle are congruent to the corresponding parts in another triangle, then the triangles are congruent.
3. Definitions of terms like corresponding parts and included angles that are used to prove triangles congruent.
Geometry 5-6 ASA and AAS
This document discusses two postulates for proving triangles congruent:
1. Angle-Side-Angle (ASA) postulate - If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
2. Angle-Angle-Side (AAS) postulate - If two angles and one non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then the triangles are congruent.
The document provides examples of applying these postulates to determine if pairs of triangles are congruent. It also notes there are no AAA or SSA postulates to prove triangles congruent.
6.6 notes
This document discusses proportionality theorems in geometry. It introduces the Triangle Proportionality Theorem, which states that if a line is parallel to one side of a triangle and intersects the other two sides, it divides them proportionally. The converse of this theorem is also presented. Two additional theorems are described: Theorem 6.6 states that if three parallel lines intersect two transversals, they divide the transversals proportionally. Theorem 6.7 states that if a ray bisects an angle of a triangle, it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides. The document provides examples and explanations of each theorem.
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This document provides information about proving triangles congruent using various postulates and theorems:
1. It describes the SSS, SAS, ASA, and AAS postulates that can be used to prove any triangles congruent, as well as the HL postulate that applies only to right triangles.
2. Examples are given to demonstrate applying each of the postulates to determine if two triangles are congruent and to find missing corresponding parts.
3. Additional theorems like CPCTC (corresponding parts of congruent triangles are congruent) and properties of vertical angles, isosceles triangles, and midpoints are also explained.
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This document discusses proving triangles congruent using various postulates and theorems, including Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), and Hypotenuse-Leg (HL). It provides examples of applying these rules to determine if triangles are congruent based on given information about angles and sides. It also contains practice problems asking to identify which postulate or theorem can be used to prove triangles congruent.
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The document discusses how to prove triangles congruent using the Side-Side-Side Postulate. It states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent. It provides examples of proving triangles congruent by showing that corresponding sides are congruent and using the Side-Side-Side Postulate.
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The document discusses five triangle congruence theorems: side-angle-side (SAS), hypotenuse-leg (HL), angle-side-angle (ASA), angle-angle-side (AAS or SAA), and provides homework assignments involving applying these theorems. It notes that the side-side-angle (SSA) and angle-angle-angle (AAA) scenarios are not sufficient on their own to prove triangle congruence.
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This document discusses different postulates and theorems for proving triangles congruent, including:
1. The Side-Side-Side (SSS) postulate, which states that if the three sides of one triangle are congruent to the three sides of another triangle, then the triangles are congruent.
2. The Side-Angle-Side (SAS) postulate, which states that if one angle and the two sides that form it in one triangle are congruent to the corresponding parts in another triangle, then the triangles are congruent.
3. Definitions of terms like corresponding parts and included angles that are used to prove triangles congruent.
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This document discusses two postulates for proving triangles congruent:
1. Angle-Side-Angle (ASA) postulate - If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
2. Angle-Angle-Side (AAS) postulate - If two angles and one non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then the triangles are congruent.
The document provides examples of applying these postulates to determine if pairs of triangles are congruent. It also notes there are no AAA or SSA postulates to prove triangles congruent.
6.6 notes
This document discusses proportionality theorems in geometry. It introduces the Triangle Proportionality Theorem, which states that if a line is parallel to one side of a triangle and intersects the other two sides, it divides them proportionally. The converse of this theorem is also presented. Two additional theorems are described: Theorem 6.6 states that if three parallel lines intersect two transversals, they divide the transversals proportionally. Theorem 6.7 states that if a ray bisects an angle of a triangle, it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides. The document provides examples and explanations of each theorem.
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This document provides information about proving triangles congruent using various postulates and theorems:
1. It describes the SSS, SAS, ASA, and AAS postulates that can be used to prove any triangles congruent, as well as the HL postulate that applies only to right triangles.
2. Examples are given to demonstrate applying each of the postulates to determine if two triangles are congruent and to find missing corresponding parts.
3. Additional theorems like CPCTC (corresponding parts of congruent triangles are congruent) and properties of vertical angles, isosceles triangles, and midpoints are also explained.
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This document discusses proving triangles congruent using various postulates and theorems, including Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), and Hypotenuse-Leg (HL). It provides examples of applying these rules to determine if triangles are congruent based on given information about angles and sides. It also contains practice problems asking to identify which postulate or theorem can be used to prove triangles congruent.
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The document discusses how to prove triangles congruent using the Side-Side-Side Postulate. It states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent. It provides examples of proving triangles congruent by showing that corresponding sides are congruent and using the Side-Side-Side Postulate.
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This document discusses properties of triangles related to side lengths and angles. It states that if one side of a triangle is longer than a second side, then the angle opposite the first side is larger than the angle opposite the second side. It also states that if one angle is larger than a second angle, then the side opposite the first angle is longer than the side opposite the second angle. The document then asks the reader to identify the longest and shortest sides of a triangle based on these properties.
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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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Conversions notes
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12.6 notes
This document contains notes from a math class lesson on the surface area and volume of spheres. It includes the objectives of being able to apply the formulas for surface area and volume of spheres. Examples are provided for students to calculate the surface area and volume of various spheres given measurements like diameters and radii. Students are assigned homework problems applying these concepts.
10.1 notes
This document discusses tangent properties of circles. It defines various circle terms like radius, diameter, chord, secant, and tangent. It presents theorems for tangents including that a tangent is perpendicular to the radius and tangent segments from outside the circle are congruent. It provides examples applying these theorems to find missing side lengths. The document instructs the reader to draw and label examples of circle terms on a worksheet.
7.6 notes
This document contains instructions for solving various mathematical formulas by transforming them to solve for different variables. It provides examples of transforming formulas for area, perimeter, rate, distance, and temperature by solving for variables like length, rate, time, and Celsius. The goal is to practice transforming formulas to solve for the desired unknown variable.
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10.5 notes
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This document discusses different triangle congruence theorems including side-angle-side (SAS), hypotenuse-leg, angle-side-angle (ASA), and angle-angle-side (AAS or SAA). It states that if two triangles have two sides and the included angle equal (SAS), or the hypotenuse and one leg equal for right triangles (hypotenuse-leg), or two angles and the included side equal (ASA), or two angles and the non-included side equal (AAS), then the triangles are congruent. It also notes that side-side-angle (SSA) is inconclusive and angle-angle-angle (AAA) only proves similarity, not
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This document summarizes the ASA and AAS postulates for proving triangle congruence. It states that if two angles and the included side of one triangle are congruent to those of another triangle, they are congruent by ASA. If two angles and a non-included side are congruent, they are congruent by AAS. It provides examples of applying these postulates to determine if triangles can be proven congruent and includes a word problem about using angles to locate a meteorite.
4.5 notes
The document discusses two triangle congruence theorems:
1) Angle-Side-Angle (ASA): If two angles and the included side of one triangle are congruent to those of another triangle, then the triangles are congruent.
2) Angle-Angle-Side (AAS): If two angles and the non-included side of one triangle are congruent to those of another triangle, then the triangles are congruent.
It also notes that Angle-Angle-Angle (AAA) only proves similarity, not congruence, and Side-Side-Angle (SSA) does not provide a conclusion.
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This document discusses congruence of triangles and the different postulates used to prove triangles are congruent. It introduces the Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), and Angle-Angle-Side (AAS) postulates. It explains that to prove triangles are congruent using SSS, all three sides must be equal; with SAS, two sides and the included angle must be equal; with ASA, two angles and the included side must be equal; and with AAS, two angles and a non-included side must be equal. The document emphasizes there is no Side-Side-Angle (SSA) or Triple-Angle
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The document discusses congruence postulates for triangles. It explains that two triangles are congruent if they meet the criteria of Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), or Angle-Angle-Side (AAS). The document provides examples of applying these postulates to determine if triangles are congruent and identifies the additional information needed.
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This document discusses triangle congruence postulates and their application. It begins by defining triangle congruence and reviewing key terms. It then explains the three triangle congruence postulates - SSS, SAS, and ASA - and provides examples of applying each one to determine if triangles are congruent. Several activities are included for students to practice identifying corresponding parts of congruent triangles and stating the postulate used. The document emphasizes that triangle congruence is important in real-life applications like architecture, art and engineering. It concludes by asking students if they have any other questions.
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4.5 notes
- 1. B E L L W O R K Is there enough given information to prove the triangles congruent? If there is, state the postulate or theorem.
- 2. 4. Angle-Side-Angle (ASA) *2 angles and the INCLUDED side I f 2 angles & the included side of one ∆ are @ to the 2 angles and included side of another ∆, then the ∆’s are @ . 5. Angle-Angle-Side (AAS or SAA) *2 angles and the NON included side I f 2 angles and the non-included side of one ∆ are @ to the 2 angles and non-included side of another ∆,then the ∆’s are @ . 4.5 Prove Triangles Congruent by ASA & AAS A B C D E F W X Y M N P
- 4. Other Scenarios 1 . Angle-Angle-Angle (AAA) *** This scenario only proves that 2 triangles are similar. *** No triangle congruency can be determined. 2. Side-Side-Angle (SSA) *** No conclusion can be made from S-S-A
- 5. HW pg. 252 #3-19 odd, 31 & 33