4-1 Congruent Figures

Quick Review

Congruent polygons have congruent corresponding parts. When you name congruent polygons, always list corresponding vertices in the same order.

Example

H I J K ≅ P Q R S . h i j k approximately equal to p q r s .  Write all possible congruence statements.

The order of the parts in the congruence statement tells you which parts correspond.

Sides: H I ¯ ≅ P Q ¯ , I J ¯ ≅ Q R ¯ , J K ¯ ≅ R S ¯ , K H ¯ ≅ S P ¯ h i bar , approximately equal to . p q bar , comma . i j bar , approximately equal to . q r bar , comma . j k bar , approximately equal to . r s bar , comma . k h bar , approximately equal to . s p bar

Angles: ∠ H ≅ ∠ P , ∠ I ≅ ∠ Q , ∠ J ≅ ∠ R , ∠ K ≅ ∠ S angle h approximately equal to . angle p comma . angle i approximately equal to . angle q comma . angle j approximately equal to . angle r comma . angle k approximately equal to . angle s

Exercises

R S T U V ≅ K L M N O . r s t u v approximately equal to k l m n o .  Complete the congruence statements.

5. T S ¯ ≅ t s bar , approximately equal to  __?__
6. ∠ N ≅ angle n approximately equal to  __?__
7. L M ¯ ≅ l m bar , approximately equal to  __?__
8. V U T S R ≅ v u t s r approximately equal to  __?__

W X Y Z ≅ P Q R S . w x y z approximately equal to p q r s .  Find each measure or length.

9. m ∠ P m angle p
10. QR
11. WX
12. m ∠ Z m angle z
13. m ∠ X m angle x
14. m ∠ R m angle r

4-2 and 4-3 Triangle Congruence by SSS, SAS, ASA, and AAS

Quick Review

You can prove triangles congruent with limited information about their congruent sides and angles.

Example

What postulate would you use to prove the triangles congruent?

You know that three sides are congruent. Use SSS.

Exercises

15. In Δ H F D , cap delta h f d comma  what angle is included between D H ¯ d h bar  and D F ¯ ? d f bar , question mark
16. In Δ O M R , cap delta o m r comma  what side is included between ∠ M angle m  and ∠ R ? angle r question mark

Which postulate or theorem, if any, could you use to prove the two triangles congruent? If there is not enough information to prove the triangles congruent, write not enough information.

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