LianetteMarie
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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

What must be given to prove that ΔBDF ΔCAEA GBH ICH and BFD CEA B segment BH is congruent to segment CH amp segment BG is congruent to segment CIC GBH ICH and B class=

Respuesta :

Dawniee
The answer is A , thank you for adding the answers

Answer:

The correct option is A.

Step-by-step 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,

[tex]\triangle BDF\sim \triangle CAE[/tex]

The required conditions are

[tex]\angle B\cong \angle C[/tex]    .... (1)

[tex]\angle D\cong \angle A[/tex]   .... (2)

[tex]\angle F\cong \angle E[/tex]     .... (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,

[tex]\angle GBH\cong \angle ICH[/tex]

[tex]\angle BFD\cong \angle CEF[/tex]

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

Option A is correct.

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