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AABC is similar to AEDC. Find v, w, x, and y. D 128° x Y 49in. B 91in. v 28° 16in. [1] wᵒ E 28in.

AABC is similar to AEDC. Find v, w, x, and y. D 128° x Y 49in. B 91in. v 28° 16in. [1] wᵒ E 28in.

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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**Title: Solving Problems Involving Similar Triangles** **Problem Statement:** Given that triangle \( \Delta ABC \) is similar to triangle \( \Delta EDC \), find the values of angles \( v \), \( w \), and the side lengths \( x \), and \( y \). **Diagram Description:** The diagram provided shows two triangles, \( \Delta ABC \) and \( \Delta EDC \), which are similar to each other. - Triangle \( \Delta ABC \): - Angle \( \angle BAC = 128^\circ \) - Angle \( \angle ACB = v^\circ \) - Side \( AB = 49 \) inches - Side \( BC = 91 \) inches - Side \( AC = x \) inches - Triangle \( \Delta EDC \): - Angle \( \angle DEC = w^\circ \) - Angle \( \angle ECD = 28^\circ \) - Side \( DE = 28 \) inches - Side \( EC = 16 \) inches - Side \( DC = y \) inches The triangles share a common angle \( \angle ACB = \angle ECD \). **To Be Determined:** - \( v = \) \( \_\_\_\_\_\_\_\_\_\_ \) - \( w = \) \( \_\_\_\_\_\_\_\_\_\_ \) - \( x = \) \( \_\_\_\_\_\_\_\_\_\_ \) inches - \( y = \) \( \_\_\_\_\_\_\_\_\_\_ \) inches **Explanation and Solution:** Since \( \Delta ABC \) is similar to \( \Delta EDC \), we can use the properties of similar triangles to find the missing values. 1. **Finding \( v \) and \( w \) (Angles):** - For \( \Delta ABC \): - We already know \( \angle BAC = 128^\circ \) - The sum of the angles in any triangle is \( 180^\circ \) - Therefore, \( \angle ACB + \angle CBA + \angle BAC = 180^\circ \) - So, \( v + 28^\circ + 128^\circ = 180^\circ \) - \( v =
Transcribed Image Text:**Title: Solving Problems Involving Similar Triangles** **Problem Statement:** Given that triangle \( \Delta ABC \) is similar to triangle \( \Delta EDC \), find the values of angles \( v \), \( w \), and the side lengths \( x \), and \( y \). **Diagram Description:** The diagram provided shows two triangles, \( \Delta ABC \) and \( \Delta EDC \), which are similar to each other. - Triangle \( \Delta ABC \): - Angle \( \angle BAC = 128^\circ \) - Angle \( \angle ACB = v^\circ \) - Side \( AB = 49 \) inches - Side \( BC = 91 \) inches - Side \( AC = x \) inches - Triangle \( \Delta EDC \): - Angle \( \angle DEC = w^\circ \) - Angle \( \angle ECD = 28^\circ \) - Side \( DE = 28 \) inches - Side \( EC = 16 \) inches - Side \( DC = y \) inches The triangles share a common angle \( \angle ACB = \angle ECD \). **To Be Determined:** - \( v = \) \( \_\_\_\_\_\_\_\_\_\_ \) - \( w = \) \( \_\_\_\_\_\_\_\_\_\_ \) - \( x = \) \( \_\_\_\_\_\_\_\_\_\_ \) inches - \( y = \) \( \_\_\_\_\_\_\_\_\_\_ \) inches **Explanation and Solution:** Since \( \Delta ABC \) is similar to \( \Delta EDC \), we can use the properties of similar triangles to find the missing values. 1. **Finding \( v \) and \( w \) (Angles):** - For \( \Delta ABC \): - We already know \( \angle BAC = 128^\circ \) - The sum of the angles in any triangle is \( 180^\circ \) - Therefore, \( \angle ACB + \angle CBA + \angle BAC = 180^\circ \) - So, \( v + 28^\circ + 128^\circ = 180^\circ \) - \( v =
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