Chapter 4 Review Proving Triangles Congruent and Isosceles

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

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

Postulates SSS If the sides of one triangle are congruent to the sides of

Postulates SSS If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. A B D C E F 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. 2

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

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

Postulates ASA If two angles and the included side of one triangle are congruent

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. A B SAS A D C E F B D C F E 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. 4

Steps for Proving Triangles Congruent 1. Mark the Given. 2. Mark … Reflexive Sides

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? 5

Problem 1 Step 1: Mark the Given Step 2: Mark reflexive sides Step 3:

Problem 1 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 Statements Step 6: Is there more? A B SSS Reasons Given Reflexive Property D C SSS Postulate 6

Problem 2 Step 1: Mark the Given Step 2: Mark vertical angles Step 3:

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 Statements Step 6: Is there more? SAS Reasons Given Vertical Angles. Given SAS Postulate 7

Problem 3 Step 1: Mark the Given Step 2: Mark reflexive sides Step 3:

Problem 3 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 Statements Step 6: Is there more? X W Y Z ASA Reasons Given Reflexive Postulate Given ASA Postulate 8

Postulates AAS If two angles and a non included side of one triangle are

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 B D C E F 9

Problem 1 Step 1: Mark the Given Step 2: Mark vertical angles Step 3:

Problem 1 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 Statements Reasons Step 6: Is there more? Given AAS Vertical Angle Thm Given AAS Postulate Lesson 4 -4: AAS & HL Postulate 10

Parts of an Isosceles Triangle l l An isosceles triangle is a triangle with

Parts of an Isosceles Triangle l l 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 Ð 1 andÐ 2 are base angles Ð 3 is the vertex angle 1 2 Base 11

Isosceles Triangle Theorems If two sides of a triangle are congruent, then the angles

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

Isosceles Triangle Theorems If two angles of a triangle are congruent, then the sides

Isosceles Triangle Theorems If two angles of a triangle are congruent, then the sides opposite those angles are congruent. A B C Example: Find the value of x. Since two angles are congruent, the A sides opposite these angles must be congruent. 3 x - 7 x+15 3 x – 7 = x + 15 2 x = 22 ° ° 50 50 B C X = 11 13