Elementary Geometry for College Students (7th Edition)

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 3 - Section 3.2 - Corresponding Parts of Congruent Triangles - Exercises - Page 150: 6

Answer

Proof for the problem: 1. $\angle 1$ and $\angle 2$ are right angles (1. Given) 2. $\angle 1\cong\angle 2$ (2. Two corresponding angles are both $90^o$) 3. $\vec{AB}$ bisects $\angle ABD$ (3. Given) 4. $\angle BAC\cong\angle BAD$ (4. The bisector of an angle separates it into 2 congruent angles) 5. $\overline{AB}\cong\overline{AB}$ (5. Identity) 6. $\triangle ABC\cong\triangle ABD$ (6. ASA)

Work Step by Step

1) First, we see that $\angle 1$ and $\angle 2$ are both right angles. Therefore, $\angle 1\cong\angle 2$ 2) It is also given that $\vec{AB}$ bisects $\angle ABD$. So, $\angle BAC\cong\angle BAD$ 3) Furthermore, by Identity, we see that $\overline{AB}\cong\overline{AB}$ Now we see that 2 angles and the included side of $\triangle ABC$ are congruent with 2 corresponding angles and the included side of $\triangle ABD$. So we would use ASA to prove triangles congruent. Now we would construct a proof for the problem: 1. $\angle 1$ and $\angle 2$ are right angles (1. Given) 2. $\angle 1\cong\angle 2$ (2. Two corresponding angles are both $90^o$) 3. $\vec{AB}$ bisects $\angle ABD$ (3. Given) 4. $\angle BAC\cong\angle BAD$ (4. The bisector of an angle separates it into 2 congruent angles) 5. $\overline{AB}\cong\overline{AB}$ (5. Identity) 6. $\triangle ABC\cong\triangle ABD$ (6. ASA)
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