CONGRUENT TRIANGLES LESSON 17(2)

CONGRUENT POSTULATES: SSS Side-Side-Side (SSS) Postulate: If all three pairs of corresponding sides of two triangles are equal, the two triangles are congruent. If you know: then you know: and you know: AB = DE BC = EF AC = DF A =  D B =  E C =  F

CONGRUENT POSTULATES: SAS Side-Angle-Side (SAS) Postulate: If two pairs of corresponding sides and the corresponding contained angles of two triangles are equal, the two triangles are congruent. If you know: then you know: and you know: AB = DE  B =  E AC = DF A =  D AC = DF C =  F

CONGRUENT POSTULATES: ASA Angle-Side-Angle (ASA) Postulate: If two angles and the contained side of one triangle are equal to two angles and the contained side of another triangle, the two triangles are congruent. If you know: then you know: and you know:  A =  D  B =  E AB = DE AC = DF C =  F BC = EF

CONGRUENT POSTULATES: RHS Right angle - Hypotenuse-Side (RHS) Postulate: If the hypotenuse and another side of one right triangle are equal to the hypotenuse and one side of a second right triangle, the two triangles are congruent. If you know: then you know: and you know:  A =  D = 90o BC = EF AC = DF B =  E C =  F AB = DE

EXAMPLE 1 In the diagram below, PA = PB and AC = BC. Explain why a) b)  APC =  BPC SOLUTION: IN , PA = PB AC = BC PC = PC Therefore (SSS) b) Since the triangles are congruent, then  APC =  BPC

YOU TRY! In the diagram below, AB = AD and BC = DC. Explain why a) b)  ABC =  ADC

SOLUTION In the diagram below, AB = AD and BC = DC. Explain why a) b)  ABC =  ADC SOLUTION: IN , AB = AD BC = DC AC = AC Therefore (SSS) b) Since the triangles are congruent, then  ABC =  ADC

EXAMPLE 2 In the diagram below, E is the midpoint of both AC and BD. Explain why AB = CD. By the Opposite Angle Theorem,  AEB =  CED SOLUTION: IN , AE = CE BE = DE Therefore (SAS) b) Since the triangles are congruent, then AB = CD

YOU TRY! In the diagram below, C is the midpoint of both KY and ZJ. Explain why KZ = YJ.

SOLUTION In the diagram below, C is the midpoint of both KY and ZJ. Explain why KZ = YJ. By the Opposite Angle Theorem,  KCZ =  YCJ SOLUTION: IN , KC = YC ZC = JC Therefore (SAS) b) Since the triangles are congruent, then KZ = YJ

EXAMPLE 3 In the diagram below, BC = ED,  OBA =  OEF, and  OCB =  ODE. Explain why  BOC =  EOD. By the Supplementary Angle Theorem,  OBC =  OED SOLUTION: IN ,  OBC =  OED BC = ED  OCB =  ODE Therefore (ASA) b) Since the triangles are congruent, then  OBC =  EOD

YOU TRY! In the diagram below, KF = ST,  ZKG =  ZTU, and  ZFK =  ZST. Explain why  KZF =  TZS.

SOLUTION In the diagram below, KF = ST,  ZKG =  ZTU, and  ZFK =  ZST. Explain why  KZF =  TZS. By the Supplementary Angle Theorem,  ZKF =  ZST SOLUTION: IN ,  ZKF =  ZTS KF = TS  ZFK =  ZST Therefore (ASA) b) Since the triangles are congruent, then  KZF =  TZS

CLASS WORK Check solutions to Lesson 17 Copy examples from this lesson Do Lesson 17(2) worksheet.