Transparency 2 Review: Lesson 4-5 Mini-Quiz. Class Greeting.

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Presentation transcript:

Transparency 2 Review: Lesson 4-5 Mini-Quiz

Class Greeting

Objective: The students will be able to write proofs using Theorems and Corollaries of Isosceles Triangles and solve problems involving Isosceles Triangles.

Chapter 4 – Lesson 6 Isosceles Triangles

Vocabulary Vertex angle (of isosceles triangle) The angle formed by the congruent sides Base angle (of isosceles triangle) The angle formed by the base and one of the congruent sides

Theorem 4.9 Isosceles triangle theorem If two sides of a triangle are congruent then the angles opposite those sides are congruent

Theorem 4.10 Conv of Isosceles triangle theorem If two angles of a triangle are congruent then the sides opposite those sides are congruent

Corollaries

Example 6-1a Write a two-column proof. Given: Prove: Proof: ReasonsStatements 1. Given1. 2. Def. of segments2. 3. Def. of isosceles  3.  ABC and  BCD are isosceles Isosceles  Theorem 5.5. Given 6.6. Substitution

Example 6-1c Write a two-column proof. Given:. Prove: Proof: ReasonsStatements 1. Given 3. Isosceles  Theorem 2. Def. of isosceles triangles  ADB is isosceles Given 5. Def. of midpoint 6. SAS 7.7. CPCTC 6.  ABC  ADC

Example 6-3a Answer: Name two congruent angles not Given.

Example 6-3b Answer: Name two congruent segments not Given. By the converse of the Isosceles Triangle Theorem, the sides opposite congruent angles are congruent. So,

Example 6-3c a. Name two congruent angles not Given. Answer: b. Name two congruent segments not Given.

Example 6-4a Each angle of an equilateral triangle measures 60°.  EFG is equilateral, and bisects bisects Find and Since the angle was bisected, so is an exterior angle of  EGJ. Answer:

Example 6-4c Subtract 75 from each side. Linear pairs are supplementary. Substitution Answer: 105  EFG is equilateral, and bisects bisects Find

b. Find x. Example 6-4d a. Answer: 90 Answer: 30  ABC is an equilateral triangle. bisects

Lesson Summary: Objective: The students will be able to write proofs using Theorems and Corollaries of Isosceles Triangles and solve problems involving Isosceles Triangles.

Preview of the Next Lesson: Objective: The students will be able to write Coordinate Proofs.

Homework Geometry 4-6