1 Chapter 4 Review Proving Triangles Congruent and Isosceles Triangles (SSS, SAS, ASA,AAS)

2 Postulates SSS If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. Included Angle:In a triangle, the angle formed by two sides is the included angle for the two sides. Included Side:The side of a triangle that forms a side of two given angles. A B C D E F

3 Included Angles & Sides Included Angle: Included Side: * **

4 Postulates ASA If two angles and the included side of one triangle are congruent to the two angles and the included side of another triangle, then the triangles are congruent. SAS If two sides and the included angle of one triangle are congruent to the two sides and the included angle of another triangle, then the triangles are congruent. A BC D E F A BC D E F

5 Steps for Proving Triangles Congruent 1.Mark the Given. 2.Mark … Reflexive Sides / Vertical Angles 3.Choose a Method. (SSS, SAS, ASA) 4.List the Parts … in the order of the method. 5.Fill in the Reasons … why you marked the parts. 6.Is there more?

6 Problem 1  StatementsReasons Step 1: Mark the Given Step 2: Mark reflexive sides Step 3: Choose a Method (SSS /SAS/ASA ) Step 4: List the Parts in the order of the method Step 5: Fill in the reasons Step 6: Is there more? AB D C SSS Given Reflexive Property SSS Postulate

7 Problem 2  Step 1: Mark the Given Step 2: Mark vertical angles Step 3: Choose a Method (SSS /SAS/ASA) Step 4: List the Parts in the order of the method Step 5: Fill in the reasons Step 6: Is there more? SAS Given Vertical Angles. SAS Postulate StatementsReasons

8 Problem 3 StatementsReasons Step 1: Mark the Given Step 2: Mark reflexive sides Step 3: Choose a Method (SSS /SAS/ASA) Step 4: List the Parts in the order of the method Step 5: Fill in the reasons Step 6: Is there more? ASA Given Reflexive Postulate ASA Postulate Z W Y X

9 Postulates AAS If two angles and a non included side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent. A BC D E F

Lesson 4-4: AAS & HL Postulate 10 Problem 1  StatementsReasons Step 1: Mark the Given Step 2: Mark vertical angles Step 3: Choose a Method (SSS /SAS/ASA/AAS/ HL ) Step 4: List the Parts in the order of the method Step 5: Fill in the reasons Step 6: Is there more? AAS Given Vertical Angle Thm AAS Postulate

11 Parts of an Isosceles Triangle An isosceles triangle is a triangle with two congruent sides. The congruent sides are called legs and the third side is called the base. 3 Leg Base 21  1 and  2 are base angles  3 is the vertex angle

12 Isosceles Triangle Theorems By the Isosceles Triangle Theorem, the third angle must also be x. Therefore, x + x + 50 = 180 2x + 50 = 180 2x = 130 x = 65 Example: x  50  Find the value of x. A B C If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

13 Isosceles Triangle Theorems If two angles of a triangle are congruent, then the sides opposite those angles are congruent. Example:Find the value of x.Since two angles are congruent, the sides opposite these angles must be congruent. 3x – 7 = x x = 22 X = 11 A B C 50   3x - 7 x+15 A B C