# Chapter 3 - Section 3.1 - Congruent Triangles - Exercises - Page 144: 29

1) Show that $\angle ABC\cong\angle ABD$. 2) Use method SAS for the following pairs: - $\angle ABC\cong\angle ABD$. - $\overline{BC}\cong\overline{BD}$ - $\overline{AB}\cong\overline{AB}$ (by Identity)

#### Work Step by Step

We have that $\overline{AB}\bot\overline{BC}$ and $\overline{AB}\bot\overline{BD}$ So $\angle ABC$ and $\angle ABD$ are both right angles, which means $\angle ABC\cong\angle ABD$. Furthermore, it is given that - $\overline{BC}\cong\overline{BD}$ - $\overline{AB}\cong\overline{AB}$ (by Identity) Now we have 2 sides and the included angle of $\triangle ABC$ are congruent with 2 corresponding sides and the included angle of $\triangle ABD$. That means according to method SAS, $\triangle ABC\cong\triangle ABD$.

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