Lesson 4-2 Some Ways to Prove Triangles Congruent (page 122) Essential Question How do you construct a proof using congruent triangles?

_______ is opposite ∠ A and … A B C opposite side

… ∠ B is opposite _______ A B C opposite angle

∠ A is the included angle between ______ and ______. A B C included angle

is the included side between ______ and ______. A B C ∠A∠A ∠B∠B included side

(1) Class Activity: using a compass, protractor, and straight edge, draw, as accurately as possible, ∆ABC with … AB = 3 cm, BC = 5 cm, and AC = 6 cm. A B C 6 cm 3 cm 5 cm Similar to page 121 #22 (d) SSS

(2) Class Activity: using a compass, protractor, and straight edge, draw, as accurately as possible, ∆DEF with … DE = 3 cm, m ∠ E = 60º, and EF = 4 cm. D F E3 cm 4 cm 60º Similar to page 121 #22 (a) SAS

(3) Class Activity: using a compass, protractor, and straight edge, draw, as accurately as possible, ∆XYZ with … m ∠ X = 30º, XY = 4 cm, and m ∠ Y = 50º. X Z Y 4 cm 30º50º Similar to page 121 #22 (b) ASA

(4) Class Activity: using a compass, protractor, and straight edge, draw, as accurately as possible, ∆UVW … m ∠ U = 30º, m ∠ V = 50º, and m ∠ W = 100º. U W V 30º50º Similar to page 121 #22 (c) AAA 100º AAA

Congruent Triangle Notes 1.If two triangles are congruent, then you know 6 pairs of corresponding parts are also congruent. 2.Based on the prior exercises, 3 pairs of congruent corresponding parts will guarantee that two triangles are congruent.

If three sides on one triangle are congruent to three sides of another triangle, then the triangles are congruent. Postulate 12 SSS Postulate

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. Postulate 13 SAS Postulate

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. Postulate 14 ASA Postulate

Ways to Prove Triangles Congruent 1. SSS Postulate 2. SAS Postulate 3. ASA Postulate Pattern that does NOT Prove △ ’s ≅ 1. AAA Know these patterns! Remember this does NOT work!

Ways to Prove Triangles Congruent SSS Postulate SAS Postulate ASA Postulate

Know and use the patterns! Classroom Exercises on pages 123 & to 11 all numbers

Ways to Prove Triangles Congruent 1. SSS Postulate 2. SAS Postulate 3. ASA Postulate Patterns that do NOT Prove △ ’s ≅ 1. AAA 2. SSA Know these patterns! Remember these do NOT work!

StatementsReasons 1.____________________________________ _____________________________________________ 2._________________________________________________________________________________ 3._________________________________________________________________________________ 4._________________________________________________________________________________ H Given: Prove: ∆ GHJ  ∆ IJH Proof: Given ∆ GHJ  ∆ IJH ∠ 1  ∠  ∠ 3  ∠  || - lines ⇒ AIA  ASA Postulate Reflexive Property (1) Complete the proof. 3 G I J

StatementsReasons 1.____________________________________ _____________________________________________ 2._________________________________________________________________________________ 3._________________________________________________________________________________ 4._________________________________________________________________________________ 1 2 O Given: Prove: ∆ MOK  ∆ TOK Proof: Given ∆ MOK  ∆ TOK ∠ 1  ∠  Def. of ∠ - Bisector SAS Postulate Reflexive Property (2) Complete the proof. M T K

Ways to Prove Triangles Congruent SSS Postulate SAS Postulate ASA Postulate

Assignment Written Exercises on pages 124 & 125 DO NOW: 1 to 15 ODD numbers GRADED: 2 to 16 EVEN numbers Also, if you have time, check out one of my links on Congruent Triangles for grades Congruent Triangles Prepare for Quiz on Lessons 4-1 and 4-2 How do you construct a proof using congruent triangles?