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Select all the true statements for triangles ABC and XYZ.

Select all the true statements for triangles ABC and XYZ.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Select all the true statements for triangles ABC and XYZ.

## Analyzing Triangles - Educational Exercise ### Objective: Select all the true statements for triangles ABC and XYZ. ### Triangles Description: #### Triangle ABC: - **Vertices**: A, B, and C - **Sides**: - AB = 12 units - BC = 16 units - AC = 20 units #### Triangle XYZ: - **Vertices**: X, Y, and Z - **Sides**: - XY = 3 units - YZ = 4 units - XZ = 5 units ### Statements to Evaluate: 1. **\<X ≅ \<C** (Angle X is congruent to Angle C) 2. **\<B ≅ \<Y** (Angle B is congruent to Angle Y) 3. **\<A ≅ \<X** (Angle A is congruent to Angle X) 4. **AB/XY = BC/XZ** (Ratio of sides AB to XY is equal to the ratio of sides BC to XZ) 5. **BC/AC = YZ/XZ** (Ratio of sides BC to AC is equal to the ratio of sides YZ to XZ) ### Instructions: Analyze the given triangles and select all statements that are true based on the congruence of angles and the ratios of corresponding sides. ### Explanations of Diagrams: 1. **Triangle ABC** is a larger triangle, with side lengths 12, 16, and 20 units respectively. 2. **Triangle XYZ** is a smaller triangle, with side lengths 3, 4, and 5 units respectively. Both triangles should be analyzed to determine congruence and similarity, based on angles and side ratios. Make sure to consider the properties of congruent triangles and the methods used to determine similarity, such as the Side-Side-Side (SSS) or Angle-Side-Angle (ASA) criteria.
Transcribed Image Text:## Analyzing Triangles - Educational Exercise ### Objective: Select all the true statements for triangles ABC and XYZ. ### Triangles Description: #### Triangle ABC: - **Vertices**: A, B, and C - **Sides**: - AB = 12 units - BC = 16 units - AC = 20 units #### Triangle XYZ: - **Vertices**: X, Y, and Z - **Sides**: - XY = 3 units - YZ = 4 units - XZ = 5 units ### Statements to Evaluate: 1. **\<X ≅ \<C** (Angle X is congruent to Angle C) 2. **\<B ≅ \<Y** (Angle B is congruent to Angle Y) 3. **\<A ≅ \<X** (Angle A is congruent to Angle X) 4. **AB/XY = BC/XZ** (Ratio of sides AB to XY is equal to the ratio of sides BC to XZ) 5. **BC/AC = YZ/XZ** (Ratio of sides BC to AC is equal to the ratio of sides YZ to XZ) ### Instructions: Analyze the given triangles and select all statements that are true based on the congruence of angles and the ratios of corresponding sides. ### Explanations of Diagrams: 1. **Triangle ABC** is a larger triangle, with side lengths 12, 16, and 20 units respectively. 2. **Triangle XYZ** is a smaller triangle, with side lengths 3, 4, and 5 units respectively. Both triangles should be analyzed to determine congruence and similarity, based on angles and side ratios. Make sure to consider the properties of congruent triangles and the methods used to determine similarity, such as the Side-Side-Side (SSS) or Angle-Side-Angle (ASA) criteria.
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