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4.7 Use Isosceles & Equilateral Triangles

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Presentation on theme: "4.7 Use Isosceles & Equilateral Triangles"— Presentation transcript:

1 4.7 Use Isosceles & Equilateral Triangles

2 Objectives Use properties of isosceles triangles
Use properties of equilateral triangles

3 Properties of Isosceles Triangles
The  formed by the ≅ sides is called the vertex angle. The two ≅ sides are called legs. The third side is called the base. The two s formed by the base and the legs are called the base angles. vertex leg leg base

4 Isosceles Triangle Theorem
Theorem 4.7 (Base Angles Theorem) If two sides of a ∆ are ≅, then the s opposite those sides are ≅ (if AC ≅ AB, then B ≅ C). A B C The Converse is also true! 

5 The Converse of Isosceles Triangle Theorem
If two s of a ∆ are ≅, then the sides opposite those s are ≅.

6 Example 1: Name two congruent angles. Answer:

7 Example 1: Name two congruent segments.
By the converse of the Isosceles Triangle Theorem, the sides opposite congruent angles are congruent. So, Answer:

8 Your Turn: a. Name two congruent angles. Answer:
b. Name two congruent segments. Answer:

9 Example 2: Write a two-column proof. Given: Prove:

10 Example 2: Proof: Reasons Statements 1. Given 1. 2. Def. of Segments
3. Def. of Isosceles  3. ABC and BCD are isosceles triangles 5. 5. Given 4. 4. Isosceles  Theorem 6. 6. Substitution

11 Your Turn: Write a two-column proof. Given: Prove:

12 Your Turn: Proof: Reasons Statements 1. Given 3. Isosceles  Theorem
2. Def. of Isosceles Triangles 1. 2. ADB is isosceles. 3. 4. 5. 4. Given 5. Def. of Midpoint 6. SAS 7. 7. CPCTC 6. ABC ADC

13 Properties of Equilateral ∆s
Corollary A ∆ is equilateral iff it is equiangular. Corollary Each  of an equilateral ∆ measures 60°.

14 Example 3a: EFG is equilateral, and bisects bisects Find and
Since the angle was bisected, Each angle of an equilateral triangle measures 60°.

15 Example 3a: is an exterior angle of EGJ. Exterior Angle Theorem
Substitution Add. Answer:

16 Example 3b: EFG is equilateral, and bisects bisects Find
Linear pairs are supplementary. Substitution Subtract 75 from each side. Answer: 105

17 Your Turn: ABC is an equilateral triangle. bisects a. Find x.
Answer: 30 b. Answer: 90

18 Assignment Geometry: Pg. 267 #3 – 30, 46


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