Review - Answers

1. They have two pairs of congruent angles so they are similar by \(A A \sim\).

2. \(1: \sqrt{3}: 2\)

3. The missing sides are 6 and \(6 \sqrt{3}\).

4. The missing sides are \(8 \sqrt{3}\) and \(16\).

5. The missing sides are \(\frac{8}{\sqrt{3}}\) and \(\frac{16}{\sqrt{3}}\).

6. They have two pairs of congruent angles so they are similar by \(A A \sim\).

7. \(1: 1: \sqrt{2}\)

8. The missing sides are both length \(3\).

9. The missing sides are \(7\) and \(7 \sqrt{2}\).

10. The missing sides are both \(\frac{7}{\sqrt{2}}\).

11. Due to parallel lines, \(\angle C B A \cong \angle D F A\) and \(\angle C A B \cong \angle D E B\). The triangles are similar by \(A A \sim\).

12. The scale factor is 2. \(x=8\).

13. \(m \angle A D B=45^{\circ}\). \(\triangle A D B\) is an isosceles right triangle.

14. \(B D=A B=3\).

15. \(A C^{2}=3^{2}+5^{2} \cdot A C=\sqrt{34}\).