4.6 Isosceles Triangles
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4.6 Isosceles Triangles. Objectives. Use properties of isosceles triangles Use properties of equilateral triangles. 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 .

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4.6 Isosceles Triangles

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4 6 isosceles triangles

4.6 Isosceles Triangles


Objectives

Objectives

  • Use properties of isosceles triangles

  • Use properties of equilateral triangles


Properties of isosceles triangles

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 thebase angles.

vertex

leg

leg

base


Isosceles triangle theorem

Isosceles Triangle Theorem

  • Theorem 4.9If two sides of a ∆ are ≅, then the s opposite those sides are ≅ (if AC ≅ AB, then B ≅ C).

A

B

C


The converse of isosceles triangle theorem

The Converse of Isosceles Triangle Theorem

  • Theorem 4.10

    If two s of a ∆ are ≅, then the sides opposite those s are ≅ (if B ≅ C, then AC ≅ AB).


Example 2

Name two congruent angles (not indicated).

Example 2:

Answer:


Example 21

Name two congruent segments (not indicated).

By the converse of the Isosceles Triangle Theorem, the sides opposite congruent angles are congruent. So,

Example 2:

Answer:


Your turn

Your Turn:

a. Name two congruent angles.

Answer:

b. Name two congruent segments.

Answer:


Properties of equilateral s

Properties of Equilateral ∆s

  • Corollary 4.3A ∆ is equilateral if it is equiangular.

  • Corollary 4.4Each  of an equilateral ∆measures 60°.


Example 3a

EFG is equilateral, and bisects bisectsFindand

Each angle of an equilateral triangle measures 60°.

Since the angle was bisected,

Example 3a:


Example 3a1

is an exterior angle of EGJ.

Example 3a:

Exterior Angle Theorem

Substitution

Add.

Answer:


Example 3b

EFG is equilateral, and bisects bisectsFind

Example 3b:

Linear pairs are supplementary.

Substitution

Subtract 75 from each side.

Answer: 105


Your turn1

ABC is an equilateral triangle. bisects

Your Turn:

a. Find x.

Answer: 30

b.

Answer: 90


Assignment

Assignment

  • Geometry:Pg. 219 #9 – 28, 36, 40

  • Pre-AP Geometry:Pg. 219 #9 – 30, 35 – 37, & 40


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