Of ∆PRQ, ∆TRS, and ∆VSQ, which are congruent? How do you know?
Hint
By the way, ∆PTV is also a triangle.
Answer
∆TRS ≅ ∆PRQ because ∆PTV is isosceles, meaning ∠T ≅ ∠P. We can use SAS to prove congruence.
If AC ≅ DF, is it true that ∆ABC ≅ ∆DEF? How do you know?
What are the three postulates (and one theorem) we can use to prove triangle congruence?
Yes, ∆ABC ≅ ∆DEF because of the AAS theorem.
Is it true that ∆LMO ≅ ∆POM? How do you know?
They share a side, don't they?
Yes, ∆LMO ≅ ∆POM because of the AAS theorem.
Is it true that ∆LMO ≅ ∆MNP? How do you know?
An awful lot of these triangles are isosceles, aren't they?
Yes, ∆LMO ≅ ∆POM because of the AAS theorem and the Isosceles Triangle Theorem.
Prove that equilateral triangles have three angles of equal measurement.
Use the Isosceles Triangle Theorem. Twice.
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