Given AADC and AAEB, What is AE? 72 A' B 55 88

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
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### Geometry Problem: Finding Segment Lengths in Right Triangles

**Problem Statement:**

Given triangles \( \triangle ADC \) and \( \triangle AEB \), what is the length of segment \( AE \)?

**Diagram Explanation:**

- The diagram features two right triangles: \( \triangle ADC \) and \( \triangle AEB \).
- Point \( A \) is common to both triangles.
- Right angles mark \(\angle AEB\) and \(\angle ADB\).
- Point \( B \) is on segment \( AC \) and separates the segment \( AC \) into segments \( AB \) and \( BC \).
- The length \( AC = 88 \) units and \( BC = 55 \) units.
- Point \( E \) creates a perpendicular from segment \( AD \) to segment \( AB \) at point \( E \), and \(\angle AEB = 90^\circ\).
- Segment \( DE \) is perpendicular to segment \( AE \).
- The length of segment \( AD \) (from point \( A \) to point \( D \)) is 72 units.

Given this setup, the goal is to find the length of segment \( AE \).

**Note for Educators:**
When attempting to solve the problem, consider using the Pythagorean theorem for each of the right triangles involved and possibly employ properties of similar triangles if necessary.
Transcribed Image Text:### Geometry Problem: Finding Segment Lengths in Right Triangles **Problem Statement:** Given triangles \( \triangle ADC \) and \( \triangle AEB \), what is the length of segment \( AE \)? **Diagram Explanation:** - The diagram features two right triangles: \( \triangle ADC \) and \( \triangle AEB \). - Point \( A \) is common to both triangles. - Right angles mark \(\angle AEB\) and \(\angle ADB\). - Point \( B \) is on segment \( AC \) and separates the segment \( AC \) into segments \( AB \) and \( BC \). - The length \( AC = 88 \) units and \( BC = 55 \) units. - Point \( E \) creates a perpendicular from segment \( AD \) to segment \( AB \) at point \( E \), and \(\angle AEB = 90^\circ\). - Segment \( DE \) is perpendicular to segment \( AE \). - The length of segment \( AD \) (from point \( A \) to point \( D \)) is 72 units. Given this setup, the goal is to find the length of segment \( AE \). **Note for Educators:** When attempting to solve the problem, consider using the Pythagorean theorem for each of the right triangles involved and possibly employ properties of similar triangles if necessary.
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