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Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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
Transcribed Image Text:### Geometry Problem and Proof Diagram
**Problem Statement:**
5. **Given:**
- \(\angle 1 \equiv \angle 2\)
- \(AB \equiv CB\)
**Show:**
- \(\triangle ADB \equiv \triangle CDB\)
**Diagram:**
- The diagram is a triangle \(ABC\) with a point \(D\) on side \(BC\), creating two smaller triangles: \(\triangle ADB\) and \(\triangle CDB\).
**Flowchart:**
1. **First Box:**
- This box is presumably the starting point of the proof, containing initial givens or assumptions based on the problem statement.
2. **Second Box:**
- Arrows indicate a logical progression from the first box to this one. It likely contains derived equalities or congruences stemming from the initial conditions.
3. **Third Box:**
- Following the same logic progression, this box would further develop the proof using previously established information.
4. **Fourth Box:**
- Two arrows pointing towards this final box suggest it contains the culmination of the logical arguments provided in the earlier steps, ultimately showing the congruence of \(\triangle ADB\) and \(\triangle CDB\).
**Explanation:**
The problem involves proving the congruence of triangles \(\triangle ADB\) and \(\triangle CDB\) using the given angle and side congruences. The flowchart provides a structured method to derive this conclusion, typically using geometric congruence postulates such as ASA (Angle-Side-Angle) or SAS (Side-Angle-Side).
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Elementary Geometry for College Students
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