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Proving Triangles Congruent SSS Postulate, SAS Postulate ASA Postulate, AAS Theorem & HL Theorem.

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Presentation on theme: "Proving Triangles Congruent SSS Postulate, SAS Postulate ASA Postulate, AAS Theorem & HL Theorem."— Presentation transcript:

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2 Proving Triangles Congruent SSS Postulate, SAS Postulate ASA Postulate, AAS Theorem & HL Theorem

3 Side - Side - Side Postulate If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.  ABC   DEF A C B F E D

4 SSS Example: E T I K  ITK     ETK

5 Side - Angle - Side Postulate If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are   JKL   MNO O N M J L K

6 SAS Example  ARK   ?  ERN K N E R A

7 Angle - Side - Angle Postulate If two angles and the included side of one triangle are  to two angles and the included side of another triangle, then the triangles are   PQR   STU U T S RQ P

8 ASA Example M Y R A AY Bisects < MAR  YMA   ?  YRA

9 Angle - Angle - Side Theorem If two angles and a nonincluded side of one triangle are  to two angles and the corresponding nonincluded side, then the triangles are   XYZ   JAC C J A Z Y X

10 AAS Example K Y R E  RKY   ?  KRE

11 Hypotenuse-Leg Theorem If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are   RPW   SBM R P W S B M

12  QMC   ?  QHC Q H C M HL Example

13 Example 1 M E K I  IEM   ?  IEK Property? SAS

14 Example 2  RBA   ?  IBT Property? ASA R T I B A

15 Example 3  MOU   ? None Property? None: SSA isn’t a property M E S U O

16 Example 4  RIK   ?  SKI Property? SSS K S I R

17 Example 5  SIL   ?  LAS Property? AAS L A S I

18  RBI   ?  GBI Property? HL I R G B Example 6

19 MISSING PARTS What information do you need to prove the following triangles are congruent by SAS? Q W E RT

20 MISSING PARTS What information do you need to prove the following triangles are congruent by ASA? A S D F G 63 o

21 MISSING PARTS What information do you need to prove the following triangles are congruent by AAS? T Y U I

22 MISSING PARTS What information do you need to prove the following triangles are congruent by SSS? Y C V B 6 6

23 MISSING PARTS What information do you need to prove the following triangles are congruent by HL? Q H C M


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