24. consider RST and XYZ shown below. Which postulate or theorem proves that the triangles are congruent **Question 24: Congruence of Triangles**Consider ∆RST and ∆XYZ shown below.Two triangles are depicted:1. Triangle RST: - Angle at vertex S is 48° - Side RS = 7 units - Side RT = 3 units 2. Triangle XYZ: - Angle at vertex Y is 48° - Side XY = 7 units - Side YZ = 3 units**Which postulate or theorem proves that the triangles are congruent?**- **A. SSS**- **B. SSA**- **C. SAS**- **D. ASA***Note:* The postulates or theorems used to prove congruence between triangles include:- **SSS (Side-Side-Side):** All three corresponding sides are equal.- **SAS (Side-Angle-Side):** Two corresponding sides and the included angle are equal.- **ASA (Angle-Side-Angle):** Two corresponding angles and the included side are equal.- **SSA (Side-Side-Angle):** Generally does not prove congruence unless specific conditions are met.*Detailed Explanation of Diagrams:*- The triangles have one side measuring 7 units and another side measuring 3 units.- Both triangles have one angle measuring 48°.- The orientation and labeling of vertices correspond in such a way that it suggests using the corresponding sides and included angle for congruence determination.**Powered by LinkIt!**

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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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24. consider RST and XYZ shown below. Which postulate or theorem proves that the triangles are congruent

**Question 24: Congruence of Triangles**

Consider ∆RST and ∆XYZ shown below.

Two triangles are depicted:
1. Triangle RST:
- Angle at vertex S is 48°
- Side RS = 7 units
- Side RT = 3 units

2. Triangle XYZ:
- Angle at vertex Y is 48°
- Side XY = 7 units
- Side YZ = 3 units

**Which postulate or theorem proves that the triangles are congruent?**
- **A. SSS**
- **B. SSA**
- **C. SAS**
- **D. ASA**

*Note:* The postulates or theorems used to prove congruence between triangles include:
- **SSS (Side-Side-Side):** All three corresponding sides are equal.
- **SAS (Side-Angle-Side):** Two corresponding sides and the included angle are equal.
- **ASA (Angle-Side-Angle):** Two corresponding angles and the included side are equal.
- **SSA (Side-Side-Angle):** Generally does not prove congruence unless specific conditions are met.

*Detailed Explanation of Diagrams:*
- The triangles have one side measuring 7 units and another side measuring 3 units.
- Both triangles have one angle measuring 48°.
- The orientation and labeling of vertices correspond in such a way that it suggests using the corresponding sides and included angle for congruence determination.

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Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

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