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4.2 Congruence and Triangles. Congruent Figures. (. B. A. ___. ___ ___ ___. ___ ___. )))). 2 figures are congruent if they have the exact same size and shape. When 2 figures are congruent the corresponding parts are congruent. (angles and sides) Quad ABDC is congruent to Quad EFHG.
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Congruent Figures ( B A ___ ___ ___ ___ ___ ___ )))) • 2 figures are congruent if they have the exact same size and shape. • When 2 figures are congruent the corresponding parts are congruent. (angles and sides) • Quad ABDC is congruent to Quad EFHG ___ ___ ___ ___ ))) (( D C F ( E ___ ___ ___ ___ ___ ___ )))) ___ ___ ___ ___ ))) (( H G
Z • If Δ ABC is to Δ XYZ, which angle is to C?
Thm 4.33rd angles thm • If 2 s of one Δ are to 2 s of another Δ, then the 3rd s are also .
Ex: find x ) ) 22o )) 87o )) (4x+15)o
Ex: continued 22+87+4x+15=180 4x+15=71 4x=56 x=14
Ex: ABCD is to HGFE, find x and y. 9cm A B E 91o F (5y-12)o 86o 113o D C H G 4x-3cm 4x-3=9 5y-12=113 4x=12 5y=125 x=3 y=25
Thm 4.4Props. of Δs A • Reflexive prop of Δ - Every Δ is to itself (ΔABC ΔABC). • Symmetric prop of Δ- If ΔABC ΔPQR, then ΔPQR ΔABC. • Transitive prop of Δ - If ΔABC ΔPQR & ΔPQR ΔXYZ, then ΔABC ΔXYZ. B C P Q R X Y Z
Given: seg RP seg MN, seg PQ seg NQ , seg RQ seg MQ, mP=92o and mN is 92o.Prove: ΔRQP ΔMQN N R 92o Q 92o P M
Statements Reasons 1. 1. given 2. mP=mN 2. subst. prop = 3. P N 3. def of s 4. RQP MQN 4. vert s thm 5. R M 5. 3rds thm 6. ΔRQP Δ MQN 6. def of Δs
