Congruent Triangles Exercises

Of ∆PRQ, ∆TRS, and ∆VSQ, which are congruent? How do you know?

Hint

By the way, ∆PTV is also a triangle.

If AC ≅ DF, is it true that ∆ABC ≅ ∆DEF? How do you know?

Hint

What are the three postulates (and one theorem) we can use to prove triangle congruence?

Is it true that ∆LMO ≅ ∆POM? How do you know?

Hint

They share a side, don't they?

Is it true that ∆LMO ≅ ∆MNP? How do you know?

Hint

An awful lot of these triangles are isosceles, aren't they?

Prove that equilateral triangles have three angles of equal measurement.

Hint

Use the Isosceles Triangle Theorem. Twice.

Statements	Reasons
1. AB ≅ BC	1. Given
2. ∠BAC ≅ ∠BCA	2. Isosceles Triangle Theorem
3. AB ≅ AC	3. Given
4. ∠ABC ≅ ∠BCA	4. Isosceles Triangle Theorem
5. m∠ABC = m∠BCA = m∠BAC	5. Definition of Congruence (2 and 4)
6. m∠ABC + m∠BCA + m∠BAC = 180	6. Angle Sum Theorem for Triangles
7. 3(m∠ABC) = 180	7. Substitution Property (5 into 6)
8. m∠ABC = 60	8. Division Property
9. All angles in and equilateral triangle are 60 degrees.	9. Substitution Property (8 into 5)