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### Geometry Construction Exercise **Given:** - Line segment \(AB\) with \(AB = 1\) **Objective:** 1. **Construct \(\triangle PQR\):** - An isosceles right triangle with a leg length of 1. 2. **Construct \(\triangle STU\):** - A 30°-60°-90° triangle with the shortest leg of length 1. **Diagram Explanation:** - A horizontal line segment is drawn and labeled \( A \) and \( B \), with \( AB = 1 \). This line segment will be used as a reference length for constructing the triangles. --- In this exercise, the goal is to use geometric construction techniques to create two specific types of triangles with given properties. The first triangle, \(\triangle PQR\), is an isosceles right triangle where the two equal legs measure 1 unit. The second triangle, \(\triangle STU\), is a 30°-60°-90° triangle where the side opposite the 30° angle (the shortest leg) is 1 unit long.

### Geometry Construction Exercise **Given:** - Line segment \(AB\) with \(AB = 1\) **Objective:** 1. **Construct \(\triangle PQR\):** - An isosceles right triangle with a leg length of 1. 2. **Construct \(\triangle STU\):** - A 30°-60°-90° triangle with the shortest leg of length 1. **Diagram Explanation:** - A horizontal line segment is drawn and labeled \( A \) and \( B \), with \( AB = 1 \). This line segment will be used as a reference length for constructing the triangles. --- In this exercise, the goal is to use geometric construction techniques to create two specific types of triangles with given properties. The first triangle, \(\triangle PQR\), is an isosceles right triangle where the two equal legs measure 1 unit. The second triangle, \(\triangle STU\), is a 30°-60°-90° triangle where the side opposite the 30° angle (the shortest leg) is 1 unit long.

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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### Geometry Construction Exercise **Given:** - Line segment \(AB\) with \(AB = 1\) **Objective:** 1. **Construct \(\triangle PQR\):** - An isosceles right triangle with a leg length of 1. 2. **Construct \(\triangle STU\):** - A 30°-60°-90° triangle with the shortest leg of length 1. **Diagram Explanation:** - A horizontal line segment is drawn and labeled \( A \) and \( B \), with \( AB = 1 \). This line segment will be used as a reference length for constructing the triangles. --- In this exercise, the goal is to use geometric construction techniques to create two specific types of triangles with given properties. The first triangle, \(\triangle PQR\), is an isosceles right triangle where the two equal legs measure 1 unit. The second triangle, \(\triangle STU\), is a 30°-60°-90° triangle where the side opposite the 30° angle (the shortest leg) is 1 unit long.
Transcribed Image Text:### Geometry Construction Exercise **Given:** - Line segment \(AB\) with \(AB = 1\) **Objective:** 1. **Construct \(\triangle PQR\):** - An isosceles right triangle with a leg length of 1. 2. **Construct \(\triangle STU\):** - A 30°-60°-90° triangle with the shortest leg of length 1. **Diagram Explanation:** - A horizontal line segment is drawn and labeled \( A \) and \( B \), with \( AB = 1 \). This line segment will be used as a reference length for constructing the triangles. --- In this exercise, the goal is to use geometric construction techniques to create two specific types of triangles with given properties. The first triangle, \(\triangle PQR\), is an isosceles right triangle where the two equal legs measure 1 unit. The second triangle, \(\triangle STU\), is a 30°-60°-90° triangle where the side opposite the 30° angle (the shortest leg) is 1 unit long.
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