Answer
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, $\triangle ABC\cong\triangle ABD$.
