Question

3. Write a similarity statement for the picture. (1 point)

Example: ∆RST ~ ∆XYZ



4. Which similarity postulate or theorem proves the triangles are similar? (1 point)




5. What are the congruent angles and/or proportional segments that justify the answer in number 4?

Answer 1

Explanation:

3. The similarity statement would be that the triangles are congruent side side side.

4. The similarity postulate is that each of the ratio of the sides are similar, such as AB:CD.

5. The ratio of the three side justifies using side-side-side similarity.

Answer 2

By the given figure,

In triangles ABC and CDE

m ∠ABC = m∠CDE = 90°

⇒ ∠ABC ≅ ∠CDE

Also, BC ║ DE ( given )

By the corresponding angles theorem,

∠ACB ≅ ∠CED

Thus, by AA similarity postulate,

`\triangle ABC\sim \triangle CDE`,

By the similarity,

`(AB)/(BC)=(BC)/(DE)=(CA)/(EC)`

3.
`\triangle ABC\sim \triangle CDE`,

4. AA similarity postulate,

5. Congruent angles are,

∠ABC ≅ ∠CDE,

∠ACB ≅ ∠CED