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Which of the following shows congruent triangles by the Angle Side Angle Postulate?

Which of the following shows congruent triangles by the Angle Side Angle Postulate?

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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Which of the following shows congruent triangles by the Angle Side Angle Postulate?

The image displays various pairs of triangles, each illustrating different geometric principles. Here's a detailed description: ### Pair 1: - **Triangles ABC and XYZ** - **Triangle ABC** shows two sides, AB and AC, marked with double lines indicating they are of equal length. - **Triangle XYZ** has sides XY and YZ marked similarly to indicate equal length with triangle ABC. ### Pair 2: - **Triangles ABC and XYZ** - **Triangle ABC** has side AC and angle B marked with single and double lines to indicate they are congruent to the corresponding side and angle in triangle XYZ. - **Triangle XYZ** shows side YZ and angle X marked to indicate congruence with triangle ABC. ### Pair 3: - **Triangles (Unnamed)** - These appear to be vertically aligned with markings indicating that the two triangles share one common side. The outer sides of each triangle are marked with double lines indicating they are of equal length. ### Pair 4: - **Triangles ABC and XYZ** - In **Triangle ABC**, two angles C and A are marked with arcs, indicating they are the same as the corresponding angles in triangle XYZ. - **Triangle XYZ** similarly shows two angles Y and Z with corresponding arcs to indicate these angles are equal to those in triangle ABC. ### Pair 5: - **Triangles ABC and DEF (Right Triangles)** - **Triangle ABC** features a right angle marked at angle C, with side AC equal to side BC. - **Triangle DEF** shows a right angle at angle F, with sides DE and DF marked with single lines to indicate equal length, similar to triangle ABC. These diagrams are utilized to demonstrate various concepts of congruent triangles and related geometric theorems, ideal for educational purposes.
Transcribed Image Text:The image displays various pairs of triangles, each illustrating different geometric principles. Here's a detailed description: ### Pair 1: - **Triangles ABC and XYZ** - **Triangle ABC** shows two sides, AB and AC, marked with double lines indicating they are of equal length. - **Triangle XYZ** has sides XY and YZ marked similarly to indicate equal length with triangle ABC. ### Pair 2: - **Triangles ABC and XYZ** - **Triangle ABC** has side AC and angle B marked with single and double lines to indicate they are congruent to the corresponding side and angle in triangle XYZ. - **Triangle XYZ** shows side YZ and angle X marked to indicate congruence with triangle ABC. ### Pair 3: - **Triangles (Unnamed)** - These appear to be vertically aligned with markings indicating that the two triangles share one common side. The outer sides of each triangle are marked with double lines indicating they are of equal length. ### Pair 4: - **Triangles ABC and XYZ** - In **Triangle ABC**, two angles C and A are marked with arcs, indicating they are the same as the corresponding angles in triangle XYZ. - **Triangle XYZ** similarly shows two angles Y and Z with corresponding arcs to indicate these angles are equal to those in triangle ABC. ### Pair 5: - **Triangles ABC and DEF (Right Triangles)** - **Triangle ABC** features a right angle marked at angle C, with side AC equal to side BC. - **Triangle DEF** shows a right angle at angle F, with sides DE and DF marked with single lines to indicate equal length, similar to triangle ABC. These diagrams are utilized to demonstrate various concepts of congruent triangles and related geometric theorems, ideal for educational purposes.
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