Question

Triangle ABC is shown BCD=30 D is a point on side AC such that BD=DA=AB prove that AD =DC

Answer 1

Explanation:

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Answer 2

<BAC=<BAD=60° (ΔABD is an equilateral triangle (all sides are equal) so each angle measures 60°)

All the angles in a triangle add to 180, so for ΔABC, we can write <ABC=180-60-30=90. So ΔABC is a right angled triangle with hypotenuse AC.

sinA=opposite/hypotenuse

sin30=AB/AC

1/2=AB/AC

AC=2AB=2AD

AC=AD+DC

AD+DC=2AD

DC=AD

QED