Question

Which best explains whether or not all isosceles triangles are similar?

a.All isosceles triangles are similar. Two angles within each triangle are always congruent.
b.All isosceles triangles are similar. The triangle sum theorem states that the sum of the angles in a triangle is 180°. Therefore, the third angle can always be determined.
c.All isosceles triangles are not similar. The pair of congruent angles within one triangle is not necessarily congruent to the pair of congruent angles within the other triangle.
d.All isosceles triangles are not similar. Given only the vertex angle of an isosceles triangle, there is not enough information to determine the measures of the base angles. Therefore, it is not possible to determine if the base angles of one isosceles triangle are congruent to the base angles of another.

Answer 1

Answer: c. All isosceles triangles are not similar. The pair of congruent angles within one triangle is not necessarily congruent to the pair of congruent angles within the other triangle.

Explanation:

An isosceles triangle is a triangle that has two sides of equal length.

Also, the isosceles theorem says that "If two sides of a triangle are congruent, then the angles opposite to these sides are congruent.

"

Consider a triangle with equal angles measure as 30°( which means the third angles will be 120°) measure and another triangle with equal angles measure as 60 ° °( which means the third angles will be 60°).

⇒ It contradicts the similarity criteria for triangle which says that in similar triangles all corresponding angles are congruent .

∴ All isosceles triangles are not similar .The pair of congruent angles within one triangle is not necessarily congruent to the pair of congruent angles within the other triangle.

Answer 2

The correct answer is:

C) All isosceles triangles are not similar. The pair of congruent angles within one triangle is not necessarily congruent to the pair of congruent angles within the other triangle.

Explanation:

Imagine we have an isosceles triangle in which the base angles are each 45°. This would make the vertex angle 90°.

Now imagine we have an isosceles triangle in which the base angles are each 30°. This would make the vertex angle 120°.

Since the angles of the first triangle are not congruent to the angles in the second triangle, the triangles are not similar.

This shows that not all isosceles triangles are similar.