Question

In the straightedge and compass construction of the equilateral triangle below, which o the following reasons can you use to prove that ABC = BCA?

Answer 1

A

Explanation:

In the figure both circles are congruence because radius AB=radius AC of one circle and radius AB = radius BC of the other circle ( radii of circles are same ). Therefore line segment AB = line segment BC= line segment AC but these are the sides of the triangle ABC. So Δ ABC is an equilateral triangle .

But we know that an equilateral Δ has three equal angles and we say that ∠ABC=∠BCA. Hence we can use the reason A, to prove the ∠ABC =∠BCA.

Answer 2

Option 1 is the correct answer.

Explanation:

In first circle AC ≅ AB radii of same triangle. Similarly in second circle sides AB ≅ BC radii of second circle.

Since AC ≅ AB and AB ≅ BC

Therefore AC ≅ BC ≅ AB

Since all the sides of the triangle ABC are equal therefore triangle is an equilateral triangle.

And we know in an equilateral triangle all the angles are equal so ∠ABC = ∠BCA.

Option 1 is the answer.