GKT101: General Knowledge for Teachers – Math

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. $A C^{2}=3^{2}+5^{2} \cdot A C=\sqrt{34}$.