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This lesson focuses on proving triangle congruence using the SSS (Side-Side-Side) and SAS (Side-Angle-Side) postulates. We will discuss the required conditions for congruence including size, shape, and polygon characteristics. Through examples, we will illustrate how to prove triangles congruent based on given information and established theorems such as the Vertical Angle Theorem. Additionally, we will assess the congruency of triangles and explore assignments involving congruence statements and their proofs.
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Week 4 Warm Up 11.07.11 Tell whether each statement is needed to show congruence: 1) The figures must have the same size. 2) The figures must be polygons. 3) The figures must have the same shape.
Postulate 19 R N S P M Q ≅ ≅ ≅ ∆MNP ≅ ∆QRS because of SSS.
Ex 1 Prove ∆PQW ≅ ∆TSW: T P W S Q , , ≅ ≅ ≅ because they are given. ∆PQW ≅ ∆TSW because of SSS.
Postulate 20 X Q ∠Q ≅∠X ≅ ≅ W Y S P ∆PQS ≅ ∆WXY because of SAS.
Ex 2 Prove ∆ABE ≅ ∆DCE: B C 1 2 E ≅ ≅ D A , Given ∠1 ≅∠2 Vertical Angle Theorem ∆AEB ≅ ∆DEC SAS Congruence Postulate
S Ex 3 Prove ∆PQR ≅ ∆PSR: Q P R ≅ they are given. 2) ≅ 1) ≅ because of the reflexive property of congruence. because of SSS. 3) ∆PQR ≅ ∆PSR
Do: 1 Is ∆PQR ≅ ∆SRQ? Give 3 congruency statement to prove it? P Q R S Assignment: Textbook Page 216, 3 - 17 all.
