4-4 Using Corresponding Parts of Congruent Triangles

Quick Review

Once you know that triangles are congruent, you can make conclusions about corresponding sides and angles because, by definition, corresponding parts of congruent triangles are congruent. You can use congruent triangles in the proofs of many theorems.

Example

How can you use congruent triangles to prove ∠ Q ≅ ∠ D ? angle q approximately equal to angle d question mark

Since Δ Q W E ≅ Δ D V K cap delta q w e approximately equal to cap delta d v k  by AAS, you know that ∠ Q ≅ ∠ D angle q approximately equal to , angle d  because corresponding parts of congruent triangles are congruent.

Exercises

How can you use congruent triangles to prove the statement true?

21. T V ¯ ≅ Y W ¯ t v bar , approximately equal to . y w bar

    

22. B E ¯ ≅ D E ¯ b e bar , approximately equal to . d e bar

    

23. ∠ B ≅ ∠ D angle b approximately equal to , angle d

    

24. K N ¯ ≅ M L ¯ k n bar , approximately equal to . m l bar

    

4-5 Isosceles and Equilateral Triangles

Quick Review

If two sides of a triangle are congruent, then the angles opposite those sides are also congruent by the Isosceles Triangle Theorem. If two angles of a triangle are congruent, then the sides opposite the angle are congruent by the Converse of the Isosceles Triangle Theorem.

Equilateral triangles are also equiangular.

Example

What is m ∠ G ? m angle g question mark

Since E F ¯ ≅ E G ¯ , ∠ F ≅ ∠ G e f bar , approximately equal to . e g bar , comma . angle f approximately equal to angle g  by the Isosceles Triangle Theorem. So m ∠ G = 30 . m angle . g equals 30 .

Exercises

Algebra Find the values of x and y.

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