Question

(b) In the figure, AABC and ACDE are equilateral triangles. Prove that: AD = BE.

Answer 1

Given

• Triangles ABC and CDE are equilateral.

We need to

• Prove that AD and BE are congruent.

Solution

Since both the given triangles are equilateral, their interior angles are each measure 60°.

Consider triangles ADC and BEC.

We have:

• AC = BC (given)
• DC = EC (given)
• ACD = ACB + BCD = 60 + BCD (angle addition)
• ECB = ECD + BCD = 60 + BCD (angle addition)

According to above, two sides and the included angle of triangles ADC and BEC are congruent by ASA.

Therefore AD = BE as corresponding sides of congruent triangles, hence proved.