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Explore the concept of congruence in triangles through properties and theorems such as the Third Angles Theorem and congruent figures. Solve geometry problems involving congruent triangles. Detailed explanations and examples included.
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4.2 Congruence and Triangles p. 202
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
A Thm 4.4Props. of Δs B • 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. 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
