1. CONGRUENT TRIANGLES
LESSON 17(2)

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

3. 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

4. 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

5. 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

6. 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

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

8. 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

9. 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

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

11. 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

12. 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

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

14. 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

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