#### Transcript Triangle Congruence by SSS and SAS

Triangle Congruence: by SSS and SAS Geometry (Holt 4-5) K. Santos Side-Side-Side (SSS) Congruence Postulate (4-5-1) If the three sides of one triangle are congruent to the three sides of another triangle , then the two triangles are congruent. A D Given: π΄πΆ β π·πΈ π΅πΆ β πΉπΈ E π΄π΅ β π·πΉ B C F Then: β π΄π΅πΆ β βπ·πΉπΈ Included Angle Included angleβis an angle formed by two adjacent sides. A B C < B is the included angle between sides π΄π΅and π΅πΆ Side-Angle-Side (SAS) Congruence Postulate (4-5-2) If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. Given: π΄π΅ β πΎπΏ π΄πΆ β πΎπ½ < A β < K A B J C K L Then: β π΄π΅πΆ β βπΎπΏπ½ Please note both angles must be included between the sides!!! ExampleβWriting a congruence statement Write a congruence statement for the congruent triangles and name the postulate you used to know the triangles were congruent. 1. D F R E T βπ·πΈπΉ β β πππ S 2. A B C βπ΄π΅πΆ β βADC SAS Postulate SSS Postulate D Exampleβwhat other information is needed What other information do you need to prove the two triangles congruent by SSS or SAS? 1. M T 2. G H U N O V Q R I S Need <M β <U for SAS or need ππ β ππ for SSS need <G β <Q for SAS or need πΌπ» β ππ for SSS Exampleβexplain triangle congruence Use the SSS or SAS postulate to explain why the triangles are congruent. A B D C It is given: π΄π΅ β πΆπ· and π΄π· β πΆπ΅ You know: π΄πΆ β πΆπ΄ by reflexive property of congruence So: βADC β βCBA by SSS Postulate Exampleβverifying triangle congruence Show that the triangles are congruent for the given value of the variable. βUVW β βYXZ, a = 3 U X 4 V ZY = a β 1 ZY = 3 β 1 ZY = 2 ππ β ππ 2 W 3 So, βUVW β βYXZ a 3a - 5 Z aβ1 XZ = a XZ =3 ππ β ππ Y XY = 3a - 5 XY = 3(3) - 5 XY = 4 ππ β ππ Proof Q Given: ππ bisects <RQS ππ β ππ Prove: βRQP β βSQP P R Statements 1. 2. 3. 4. ππ bisects <RQS < RQP β < SQP ππ β ππ ππ β ππ 5. βRQP β βSQP 1. 2. 3. 4. S Reasons Given Definition of angle bisector Given Reflexive property of congruence 5. SAS Postulate (3, 2, 4) Proof πΈπΊ || π»πΉ πΈπΊ β π»πΉ Prove: βUVW β βYXZ Given: E G F Statements 1. πΈπΊ || π»πΉ 2. < EGF β <HFG 1. 2. 3. πΈπΊ β π»πΉ 4. πΉπΊ β πΊπΉ 3. 4. 5. βUVW β βYXZ 5. H Reasons Given Alternate Interior Angles Theorem Given Reflexive Property of congruence SSS Postulate (2, 3, 4)