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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Transcribed Image Text:**Question:**
What information is needed to prove the two triangles congruent by SAS (Side-Angle-Side)?
**Diagram:**
The diagram shows two triangles, \(\triangle ABC\) and \(\triangle ADC\), sharing a common vertex \(A\) and a common side \(AC\). The triangles are adjacent, with point \(C\) being on line segment \(BD\).
**Option A:**
\(\angle BAD \cong \angle CDA\)
**Option B:**
\(\angle BAC \cong \angle DAC\)
**Option C:**
\(AC \perp BD\)
**Option D:**
\(AB \cong AD\)
**Answer Choices:**
- \( \bigcirc \) A
- \( \bigcirc \) B
- \( \bigcirc \) C
- \( \bigcirc \) D
**Explanation for SAS (Side-Angle-Side) Criterion:**
To prove that two triangles are congruent using the SAS criterion, you need two pairs of congruent sides and the included angle (the angle between the two sides) to be congruent. Determine which option provides the necessary information to satisfy these conditions.
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