Question

What must be given to prove that ΔBDF ~ ΔCAE?

A.)  ∠GBH ≅ ∠ICH and ∠BFD ≅ ∠CEA

B.)  segment BH is congruent to segment CH & segment BG is congruent to segment CI

C.) ∠GBH ≅ ∠ICH and ∠BIG ≅ ∠CGJ

  


D.)  segment BH is congruent to segment CH & segment HG is congruent to segment HI

Answer 1

The answer is A , thank you for adding the answers

Answer 2

The correct option is A.

Explanation:

We have to prove ΔBDF and ΔCAE are similar.

Two triangles are called similar if their corresponding interior angles are same or the corresponding sides are in a proportion.

According to the property of similarity, if two corresponding angles of triangles are same then the triangles are similar.

To prove,

`\triangle BDF\sim \triangle CAE`

The required conditions are

`\angle B\cong \angle C` .... (1)

`\angle D\cong \angle A` .... (2)

`\angle F\cong \angle E` .... (3)

If any two conditions from the above mentioned conditions are given then we can say that the ΔBDF and ΔCAE are similar.

Only option A satisfies the condition 1 and 3 because,

`\angle GBH\cong \angle ICH`

`\angle BFD\cong \angle CEF`

If these angles are congruent, then by AA rule of similarity ΔBDF and ΔCAE are similar.

Option A is correct.