4-2 Triangle Congruence by SSS and SAS

Objective

To prove two triangles congruent using the SSS and SAS Postulates

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In the Solve It, you looked for relationships between corresponding sides and angles. In Lesson 4-1, you learned that if two triangles have three pairs of congruent corresponding angles and three pairs of congruent corresponding sides, then the triangles are congruent.

If you know…

• ∠ F ≅ ∠ J angle f approximately equal to . angle j
• ∠ G ≅ ∠ K angle g approximately equal to . angle k
• ∠ H ≅ ∠ L angle h approximately equal to . angle l
• F G ¯ ≅ J K ¯ f g bar , approximately equal to . j k bar
• G H ¯ ≅ K L ¯ g h bar , approximately equal to . k l bar
• F H ¯ ≅ J L ¯ f h bar , approximately equal to . j l bar

…then you know Δ F G H ≅ Δ J K L . cap delta f g h approximately equal to cap delta j k l .

However, this is more information about the corresponding parts than you need to prove triangles congruent.

Essential Understanding You can prove that two triangles are congruent without having to show that all corresponding parts are congruent. In this lesson, you will prove triangles congruent by using (1) three pairs of corresponding sides and (2) two pairs of corresponding sides and one pair of corresponding angles.

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