Chapter 4 Review Proving Triangles Congruent and Isosceles
- Slides: 13
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 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
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 / 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: 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: 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: 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 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: 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 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 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 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
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