Given the triangles below, fill in the blanks with the appropriate information The image depicts two triangles, △TRS and △UVW, with specific side lengths and angles given in algebraic expressions.**Triangle △TRS:**- Angle T is labeled \((2x + 20)^\circ\).- Side TR is labeled \(x + 6\).- Side RS is labeled \(2x + 10\).**Triangle △UVW:**- Angle U is labeled \((x + 50)^\circ\).- Side UV is labeled \(3x - 20\).- Side VW is labeled \(2x - 24\).There is a series of fill-in-the-blank questions below the triangles:1. "The triangles are congruent by [type your answer] and the measure of RT is [type your answer]."2. "UV is [type your answer], and the measure of angle R is [type your answer] degrees."The task is to determine the conditions under which these triangles are congruent and calculate specific measurements.

Answered: (x + 50)° (2x + 20)° 2x - 24 十 * +6 W…

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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Given the triangles below, fill in the blanks with the appropriate information

The image depicts two triangles, △TRS and △UVW, with specific side lengths and angles given in algebraic expressions.

**Triangle △TRS:**
- Angle T is labeled \((2x + 20)^\circ\).
- Side TR is labeled \(x + 6\).
- Side RS is labeled \(2x + 10\).

**Triangle △UVW:**
- Angle U is labeled \((x + 50)^\circ\).
- Side UV is labeled \(3x - 20\).
- Side VW is labeled \(2x - 24\).

There is a series of fill-in-the-blank questions below the triangles:
1. "The triangles are congruent by [type your answer] and the measure of RT is [type your answer]."
2. "UV is [type your answer], and the measure of angle R is [type your answer] degrees."

The task is to determine the conditions under which these triangles are congruent and calculate specific measurements.

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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