Exercises 1. In the figure, E is the midpoint of AB and CD, and AB=CD. Write a paragraph proof to prove that AE ED. E is the midpoint of AB and CD, and AB=CD

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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Write a paragraph proof to prove that AE ≅ ED.
**Exercises**

1. In the figure, E is the midpoint of \( \overline{AB} \) and \( \overline{CD} \), and \( AB = CD \). Write a paragraph proof to prove that \( \triangle AE \cong \triangle ED \).

   _E is the midpoint of \( \overline{AB} \) and \( \overline{CD} \), and \( AB = CD \)._

2. Given that S is the midpoint of \( \overline{QP} \), T is the midpoint of \( \overline{PR} \), and P is the midpoint of \( \overline{ST} \), write a paragraph proof to show that \( QS = TR \).

**Diagram Explanation:**

The image includes a simple geometric figure with points A, B, C, D, and E. There are line segments \( \overline{AB} \) and \( \overline{CD} \) with E marked as their midpoint. The layout suggests congruent line segments, with lines drawn to emphasize the geometric relationships being described.
Transcribed Image Text:**Exercises** 1. In the figure, E is the midpoint of \( \overline{AB} \) and \( \overline{CD} \), and \( AB = CD \). Write a paragraph proof to prove that \( \triangle AE \cong \triangle ED \). _E is the midpoint of \( \overline{AB} \) and \( \overline{CD} \), and \( AB = CD \)._ 2. Given that S is the midpoint of \( \overline{QP} \), T is the midpoint of \( \overline{PR} \), and P is the midpoint of \( \overline{ST} \), write a paragraph proof to show that \( QS = TR \). **Diagram Explanation:** The image includes a simple geometric figure with points A, B, C, D, and E. There are line segments \( \overline{AB} \) and \( \overline{CD} \) with E marked as their midpoint. The layout suggests congruent line segments, with lines drawn to emphasize the geometric relationships being described.
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