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

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,

The required conditions are

   .... (1)

  .... (2)

    .... (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,

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

Option A is correct.

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation:

answer is 144

step-by-step explanation: