The angles opposite the congruent sides of an isosceles triangle are congruent. PLZ HELP
Is this a true/false question? What is being asked here?
Yes, it is true.
Commonly referred to as the "Isosceles Triangle Theorem" or ITT
If two sides of a triangle are equal, the angles opposite the sides are equal.
Absolutely! I'd be happy to help you with that.
To prove that the angles opposite the congruent sides of an isosceles triangle are congruent, we can use the properties of triangle angles and congruence.
Here's how you can prove it step by step:
Step 1: Start with an isosceles triangle. An isosceles triangle has two sides of equal length.
Step 2: Label the triangle. For the sake of explanation, let's call it triangle ABC, where AB = AC.
Step 3: Let's say that angle A is the vertex angle (the angle between the two congruent sides AB and AC) and angles B and C are the base angles (the angles opposite to the congruent sides).
Step 4: Now, our goal is to prove that angle B is congruent to angle C.
Step 5: Since AB = AC (given in an isosceles triangle), we can use the property of isosceles triangles that the angles opposite to the congruent sides are congruent.
So, angle B and angle C are congruent (B ≅ C).
That's it! We have just proved that the angles opposite the congruent sides of an isosceles triangle are congruent.