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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Question

Transcribed Image Text:**Find z:**
In the provided image, we have a triangle with another smaller triangle inside it. The larger triangle has sides of length \(z\), \(16\), and \(8\).
The smaller triangle, which is located at the top part of the larger triangle, has sides of \(7\), \(8\), and \(8\). One of its vertices coincides with the top of the larger triangle, and its base is parallel to the base of the larger triangle.
Given:
- One side of the smaller triangle is labeled \(7\).
- The base of the larger triangle, spanning \(z\) and \(16\), is divided into two segments: \(16\) and \(8\).
- The other two sides of the larger triangle are each labeled \(8\), and the smaller triangle shares one of these sides.
To find the missing length \(z\).
To understand the context, these triangles share similar properties that could involve the principles of similar triangles or the Pythagorean theorem depending on the given information. However, with the values provided and the similarity in structure, the property of proportionality in similar triangles may come into play.
\( z = \frac{7}{8} * 16 \)
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