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Find the measure of 4ACB for the congruent triangles ABC and A'B'C'.

Find the measure of 4ACB for the congruent triangles ABC and A'B'C'.

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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**Congruent Triangles: Finding the Measure of \(\angle ACB\)** In this problem, we have two congruent triangles, \(\triangle ABC\) and \(\triangle A'B'C'\). The task is to find the measure of \(\angle ACB\). ### Triangles Details: 1. **Triangle \(A'B'C'\):** - Side \(C'B'\) measures 34 units. - \(\angle A'C'B'\) is \(36^\circ\). 2. **Triangle \(ABC\):** - Side \(BC\) measures 31 units. - Side \(AB\) measures 20 units. - \(\angle BAC\) is \(85^\circ\). ### Problem: Find the measure of \(\angle ACB\). \(\angle ACB = \square^\circ\) ### Explanation: Since \(\triangle ABC\) and \(\triangle A'B'C'\) are congruent, corresponding angles and sides are equal. Thus, you can use the properties of congruent triangles to find missing angles or side lengths. To solve, one strategy would be: - Use the fact that the sum of angles in a triangle is \(180^\circ\). - In \(\triangle ABC\), calculate \(\angle ACB\) using the known angles and the sum of angles in a triangle. **Note:** The actual calculations are not shown here, but students should perform the steps to find \(\angle ACB\) using basic geometric principles.
Transcribed Image Text:**Congruent Triangles: Finding the Measure of \(\angle ACB\)** In this problem, we have two congruent triangles, \(\triangle ABC\) and \(\triangle A'B'C'\). The task is to find the measure of \(\angle ACB\). ### Triangles Details: 1. **Triangle \(A'B'C'\):** - Side \(C'B'\) measures 34 units. - \(\angle A'C'B'\) is \(36^\circ\). 2. **Triangle \(ABC\):** - Side \(BC\) measures 31 units. - Side \(AB\) measures 20 units. - \(\angle BAC\) is \(85^\circ\). ### Problem: Find the measure of \(\angle ACB\). \(\angle ACB = \square^\circ\) ### Explanation: Since \(\triangle ABC\) and \(\triangle A'B'C'\) are congruent, corresponding angles and sides are equal. Thus, you can use the properties of congruent triangles to find missing angles or side lengths. To solve, one strategy would be: - Use the fact that the sum of angles in a triangle is \(180^\circ\). - In \(\triangle ABC\), calculate \(\angle ACB\) using the known angles and the sum of angles in a triangle. **Note:** The actual calculations are not shown here, but students should perform the steps to find \(\angle ACB\) using basic geometric principles.
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