Question

Question 1 (1 point)
This diagram is a straightedge and compass construction. A is the center
of one circle,
and B is the center of the other. Explain how we know triangle ABC is
equilateral.

Answer 1

Answer/Step-by-step explanation:

Segments AB and AC are both radii of the circle with center A. All radii of a circle are always equal, tgerefire,:

$AB = AC$

Segments AB and BC are both radii of the circle with center B. All radii of a circle are always equal, therefore:

$AB = BC$

Thus,

$AB = AC = BC$

∆ABC has sides AB, AC, and BC, which are all equal (equal radii).

Therefore, ∆ABC is an equilateral triangle.

An equilateral triangle has 3 equal sides.