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This resource explores the concept of congruence in geometric figures, focusing on triangles and quadrilaterals. It explains that two figures are congruent if they share the same size and shape, detailing how corresponding parts (angles and sides) are also congruent. The document includes key theorems, such as the Angles Theorem, demonstrating that if two angles of one triangle are equal to two angles of another triangle, then the third angles are also equal. It provides examples and proofs to aid in understanding these principles.
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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
