Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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### Week 2 Day 1 HW

1. ![Triangle Diagram](your_image_url)
   
   **Given:** 
   - \( \triangle ABD \) and \( \triangle ACD \) are two right triangles with \( \angle ADB = \angle ADC = 90^\circ \).
   - \( \overline{AB} \cong \overline{AC} \).

   **To Show:** 
   - Prove that \( \triangle ABD \cong \triangle ACD \), and state which criterion is used.

### Explanation:
In the diagram, triangle \( ABC \) is given with a perpendicular line \( AD \) from point \( A \) to side \( BC \). This creates two right triangles, \( \triangle ABD \) and \( \triangle ACD \).

- Since \( AD \) is perpendicular to \( BC \):
  - \( \angle ADB = \angle ADC = 90^\circ \).

- \( \overline{AB} \cong \overline{AC} \) by the given condition.

To prove that \( \triangle ABD \cong \triangle ACD \), we can use the RHS (Right-angle Hypotenuse Side) criterion:
  
- Both triangles have a right angle.
- Hypotenuses \( \overline{AB} \) and \( \overline{AC} \) are congruent.
- Side \( \overline{AD} \) is common for both triangles.

Thus, both triangles are congruent by the RHS criterion.
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Transcribed Image Text:### Week 2 Day 1 HW 1. ![Triangle Diagram](your_image_url) **Given:** - \( \triangle ABD \) and \( \triangle ACD \) are two right triangles with \( \angle ADB = \angle ADC = 90^\circ \). - \( \overline{AB} \cong \overline{AC} \). **To Show:** - Prove that \( \triangle ABD \cong \triangle ACD \), and state which criterion is used. ### Explanation: In the diagram, triangle \( ABC \) is given with a perpendicular line \( AD \) from point \( A \) to side \( BC \). This creates two right triangles, \( \triangle ABD \) and \( \triangle ACD \). - Since \( AD \) is perpendicular to \( BC \): - \( \angle ADB = \angle ADC = 90^\circ \). - \( \overline{AB} \cong \overline{AC} \) by the given condition. To prove that \( \triangle ABD \cong \triangle ACD \), we can use the RHS (Right-angle Hypotenuse Side) criterion: - Both triangles have a right angle. - Hypotenuses \( \overline{AB} \) and \( \overline{AC} \) are congruent. - Side \( \overline{AD} \) is common for both triangles. Thus, both triangles are congruent by the RHS criterion.
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