Question

6.
es to complete the sentence.
on to determine if the following
, could possibly be true, or definitely
and a right triangle are similar.
be true. a right triangle has a 90°
angle in it, and an equilateral triangle
have a 90° angle. they
be similar,
as corresponding angles in similar figures must have the
same measure.

Explanation:

Step1: Properties of equilateral triangle

An equilateral triangle has all angles equal to \(60^{\circ}\) as the sum of angles in a triangle is \(180^{\circ}\) and \(180\div3 = 60\).

Step2: Similarity condition

For two triangles to be similar, their corresponding angles must be equal. A right - triangle has a \(90^{\circ}\) angle and an equilateral triangle has no \(90^{\circ}\) angle.

Answer:

A right triangle has a \(90^{\circ}\) angle in it, and an equilateral triangle definitely cannot have a \(90^{\circ}\) angle. They definitely cannot be similar, as corresponding angles in similar figures must have the same measure.