Chapter 6: Triangles

Questions

1. $\triangle ABC\sim\triangle DEF$: $AB=4, DE=6$, area$(ABC)=32$. Find area$(DEF)$.
2. Legs $9, 12$; hypotenuse?
3. State BPT converse.
4. Similar triangles side ratio $2:3$. Area ratio?
5. Right triangle legs $5, 12$. Hypotenuse.
6. State Pythagoras theorem.
7. $D, E$ on $AB, AC$: $AD = 1.5, DB = 3, AE = 1, EC = 2$. Is $DE\parallel BC$?
8. Altitudes of two similar triangles are in ratio $5:3$. Area ratio?
9. In $\triangle ABC$ right at $B$: $AB = 6, BC = 8$. Find $AC$.
10. Two similar triangles have perimeters $30$ cm and $20$ cm. If one side of first is $12$ cm, find the corresponding side of the second.

Extra Practice (Optional)

• State RHS congruence.
• Draw a triangle similar to $\triangle ABC$ with scale $3/4$.
• Pythagoras converse: are sides $7, 24, 25$ right-angled?
• Area ratio if scale factor is $1/2$.
• Prove: in a right triangle, altitude to hypotenuse creates two triangles similar to original.