Question

Determine whether the triangles are similar. If so, write a similarity
statement.

Answer 1

`\triangle FED\sim \triangle JEH`

Explanation:

Both pairs of vertical angles formed at point E are equal. Therefore, the two triangles share two angles. If two triangles share two angles, they must also share the third angle, since the sum of the interior angles of a triangle add up to 180 degrees. Therefore, all three angles of the two triangles are equal, which is a proof of similarity.
`\implies \boxed{\triangle FED\sim \triangle JEH}`

Answer 2

9514 1404 393

Answer:

ΔDEF ~ ΔHEJ

Explanation:

The vertical angles at E are congruent, and the marked angles at F and J are congruent. The two triangles are similar by the AA postulate.

The given portion of the similarity statement names the angles in the order "unspecified", "vertical", and "50°". If we name those angles in the same order in the other triangle, the similarity statement becomes ...

ΔDEF ~ ΔHEJ