Question

Consider that △ABC is an equilateral triangle, and AD is a perpendicular bisector of △ABC. Equilateral triangle A B C is cut by perpendicular bisector A D. If AB = 2x, complete the statements below. 2 + (AD)2 = (2x)2 (AD)2 = x2 – x2 (AD)2 = x2 AD =

Answer 1

X

4

3

X

Explanation:

Correct on Edge 2020

Answer 2

Answer: AD = x√3

AD² = 3x²

Explanation:

If ΔABC is equilateral and is cut by a perpendicular, then the resulting two triangles (ΔBDA & ΔBDC) are both 30°-60°-90° triangles where

∠A = 30°

∠D = 90°

∠B = ∠C = 60°

In a 30° - 60° - 90° triangle, the corresponding sides have lengths of

↓ ↓ ↓

b b√3 2b

Thus: BD = CD = b

AD = b√3

AB = AC = 2b

Since it is given that AB = 2x, replace the "b" above" with an "x"

BD = x, CD = x

AD = x√3

AB = 2x, AC = 2x

I'm not sure what the statements are because they are squished together but hopefully the information I provided will allow you to finish answering the question.