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## Side-Side-Side (SSS) Congruence

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**Chapter 4.4 Proving triangle congruence SSS,SASObjective:**Use the SSS and SAS postulates for proving angle congruence. Check.4.35 Prove that two triangles are congruent by applying the SSS, SAS, ASA, AAS, and HL congruence statements. CLE 3108.4.4 Develop geometric intuition and visualization through performing geometric constructions with straightedge/compass and with technology. CLE 3108.4.8 Establish processes for determining congruence and similarity of figures, especially as related to scale factor, contextual applications, and transformations.**Forget past mistakes. Forget failures. Forget everything**except what you're going to do now and do it." William Durant Side-Side-Side (SSS) Congruence • If the sides of one triangle are congruent to the sides of a second triangle then the triangles are congruent. • ABC FDE Side-Angle-Side (SAS) Congruence • If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent • ABC FDE F F A D A D E E C B B C**Constructions – Congruent Triangles Using Sides**Y • Draw a triangle, label the vertices X, Y, and Z • Elsewhere on the paper, use a straight edge to construct segment RS Such that RS XZ • Using R as the center, draw and arc with radius equal to XY • Using S as the center draw and arc with a radius equal to YZ. • Let T be the point of intersection of the two arcs. • Draw RT and ST to form RST Z X T R S**Constructions – Congruent Triangles using 2 sides and an**included angle C A • Draw a triangle, label the vertices A, B, and C • Elsewhere on the paper, use a straight edge to construct segment KL Such that KL BC • Construct and angle congruent to B using KL as a side of the angle and K as the vertex. • Construct JK such that JK BA. • Draw JL to complete KJL B J K L**Copy the two Triangles using the requested methodology**B E Using Sides create STV ABC Using 2 sides and an included angle create XYZ DEF D A C F**Can you prove Congruence?**Side, Side, Side - SSS**Can you prove Congruence?**Side, Angle, Side - SAS**Can you prove Congruence?**Not enough Information**Can you prove Congruence?**Not enough Information**Can you prove Congruence?**Either SSS or SAS**B**C 4 $ 3 Page 197 34. 2 Given: ABCD, ADCB, ADDC, ABBC, AD|| BC, AB|| CD 1 A D Prove: ACD CAB Statement • ABCD, ADCB • AC CA • ADDC, ABBC • AD|| BC, AB|| CD • D and B is a right Angle • 1 4, 2 3 • D B • ACD CAB Reason • Given • Transitive Property • Given • Given • Definition of lines • Alternate Interior ’s are • Definition of Right Angles • Def of congruent triangles**Y**C B Given: ABAC,BYCY Prove: BYA CYA A Statement Reason Given Reflexive Property SSS • ABAC,BYCY • AY AY • BYA CYA**A**D Given: X is the midpoint of BD, X is the midpoint of ACProve: DXC BXA X Statement Reason Given Definition of Midpoint Vertical Angles are SAS B C • X is the midpoint of BD, X is the midpoint of AC • DX XB, CX XA • DXC BXA • DXC BXA**Practice Assignment**• Block Page 267, 10 – 18 even • Honors; Page 267, 10 – 28 even