REFERENCE/MY INFO: https://www.youtube.com/watch?v=vGuiy7NnJlM

Proving Triangle Congruence Reference from book (PIs read) Here's a very simple example showing how the SSS Postulate is used in proving triangle congruence. EXAMPLE 1 Given: Square LOVE and its diagonal LV Prove: ALEV = ALOV SOLUTION: Proof : Statements Reasons 1. Square LOVE, LV is a diagonal. 1. Given 2. LE = LO; LO = VE 2. Definition of Square 3. Reflexive Property of 3. LV = LV Congruence 4. ALEV = ALOV 4. SSS Postulate (2, 3) Try This orlions do sig Given: Rhombus PRAY and its diagonal RY . Prove: ARPY = ARAY sbia Activity 2 suggests the SAS Postulate. SIDE-ANGLE-SIDE (SAS) POSTULATE If two sides and the included angle of one triangle are congruent to corresponding two sides and included angle of another triangle, then the two triangles are congruent. EXAMPLE 2 Given: ABOW and ABAT; B is the midpoint of OA and TW. Prove: ABOW = ABAT Plan: You know that TB = BW and OB = BA. To use SAS Postulate, you need to establish that their included angles are congruent, and they are since the angles are vertical. Hence, ABOW = ABAT. Let's write this proof formally.SOLUTION: Proof: Statements 1. B is the midpoint of OA and TW. Reasons 1. Given 2. TB = WB and OB = AB 3 . LOBW and ZABT are vertical 2. Definition of Midpoint angles. 3. Definition of Vertical Angles 4. LOBW = LABT 5 . ABOW = ABAT 4. Vertical angles are congruent. 5 . SAS Postulate (2, 4) Try This Given: Isosceles ABOX, with vertex at O, and its median OT . Prove: ABOT = AXOT Activity 3 suggests the ASA Postulate. ANGLE-SIDE-ANGLE (ASA) POSTULATE If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. EXAMPLE 3 Given: APET and APAT LETP = LATP LEPT = ZAPT Prove: APET = APAT T SOLUTION: Proof: Reasons Statements 1. LETP = LATP; LEPT = ZAPT 1. Given 2. Reflexive Property of Congruence 2. PT = PT 3. ASA Postulate (1, 2) 3. APET = APAT Iry This Given: AHOT and AMET; T is a midpoint of OE; ZO and LE are right angles. Prove: AHOT = AMET LESSON 7.3 Triangle CongruActivity 4 suggests the SAA Postulate. SIDE-ANGLE-ANGLE (SAA) POSTULATE If two angles of a triangle and a side opposite one of its angles are congruent to two angles and a side opposite one of the angles of another triangle, then the two triangles are congruent. EXAMPLE 4 Given: ABLU is an isosceles triangle. LE is perpendicular to BU. B E Prove: ABLE = AULE SOLUTION: Proof: Statements Reasons 1. ABLU is an isosceles triangle. 1. Given 2. BL = UL 2. Definition of Isosceles Triangle 3. Base angles of an isosceles 3. LB= LU triangle are = 4. LE is perpendicular to BU. 4. Given 5. LBEL and ZUEL are right 5. Definition of perpendicularity angles. 6. ZBEL = LUEL 6. Right angles are congruent ? Think 7. ABLE = AULE 7. SAA Postulate (2, 3, 6) About This Note that the SAA Postulate may also be treated as a theorem. It can be proven Can you guarantee the congruence using the other triangle congruence postulates. between two Try This triangles whose corresponding Given: GOLD is a rectangle. angles are congruent? Why or GL is a diagonal; ZOGL = LDLG. O why not? Prove: AGDL = ALOG Reflect Fret no more! I'm so poor at proving tasks. Mistakes can be powerful. They are I make so many important for our mind's growth. The one mistakes! I'll never get it who makes the most mistakes, and never right. gives up, learns the most.Answer: Exercises Comprehension Check Name the required side or angle. 1. the included side of LR and ZRAY M 2. the included angle of MA and EM the angle opposite AY 4. the side opposite ZM State whether the triangles are congruent or not. If the triangles are congruent, write a congruence statement and name the postulate that guarantees congruence between each pair of triangles. 5. G 10. or H W 6. 11. M P R 7. 12. M N O Q B 8. 13. D D S CO RCommunicating 14. What is the advantage of using the triangle-congruence postulates in establishing congruence between triangles? YASS bus All lo sbis b 15. As a lantern-maker, Noemi makes congruent triangles Mil bas, AM to s without ever using a protractor. How does she make sure that the triangles are congruent? What postulate guarantees that the triangles are congruent? sfizoggo phProving Triangle Congruence Kuta Software - Infinite Geometry Name SSS, SAS, ASA, and AAS Congruence Date Period State if the two triangles are congruent. If they are, state how you know. 2) 3) 4) 5) 6) 7) 8) 9) 10) HHState what additional information is required in order to know that the triangles are congruent for the reason given. 11) ASA 12) SAS K W V 13) SAS 14) ASA L B K E K 15) SAS 16) ASA T H T S M K 17) SSS 18) SAS R U K W V D M