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Liono4ka [1.6K]
2 years ago
10

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

Mathematics
1 answer:
TiliK225 [7]2 years ago
8 0
<h3>Given</h3>

  • Triangles ABC and CDE are equilateral.

<h3>We need to </h3>

  • Prove that AD and BE are congruent.

<h3>Solution</h3>

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

Consider triangles ADC and BEC.

<u>We have:</u>

  • 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.

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