Question

in the figure shown, the measures of all angles are equal, and ab = ef.
what type of triangle is △abc?
what type of triangle is △def?
select all that apply
a. △abc right; △def right
b. △abc equilateral; △def equilateral
c. △abc isosceles; △def isosceles
d. △abc scalene; △def scalene

Explanation:

1. For $\triangle ABC$: All angles are equal, so by the property of triangles, if all interior angles are equal, the triangle is equilateral (all sides equal). An equilateral triangle is also a special case of an isosceles triangle (has at least two equal sides).
2. For $\triangle DEF$: All angles are equal to those of $\triangle ABC$, so its angles are also equal, making it equilateral. Additionally, $AB=EF$, and since $AB$ is a side of an equilateral triangle, $EF$ equals the sides of $\triangle ABC$, so all sides of $\triangle DEF$ are equal. It is also a special isosceles triangle.
3. Right triangles have a 90° angle, which contradicts all angles being equal (each angle would be 60° here). Scalene triangles have no equal sides/angles, which also does not fit.

Answer:

B. $\triangle ABC$ equilateral, $\triangle DEF$ equilateral
C. $\triangle ABC$ isosceles, $\triangle DEF$ isosceles