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4.6 Isosceles Triangles

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4.6 Isosceles Triangles

- Use properties of isosceles triangles
- Use properties of equilateral 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

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

A

B

C

- Theorem 4.10
If two s of a ∆ are ≅, then the sides opposite those s are ≅ (if B ≅ C, then AC ≅ AB).

Name two congruent angles (not indicated).

Answer:

Name two congruent segments (not indicated).

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

Answer:

a. Name two congruent angles.

Answer:

b. Name two congruent segments.

Answer:

- Corollary 4.3A ∆ is equilateral if it is equiangular.
- Corollary 4.4Each of an equilateral ∆measures 60°.

EFG is equilateral, and bisects bisectsFindand

Each angle of an equilateral triangle measures 60°.

Since the angle was bisected,

is an exterior angle of EGJ.

Exterior Angle Theorem

Substitution

Add.

Answer:

EFG is equilateral, and bisects bisectsFind

Linear pairs are supplementary.

Substitution

Subtract 75 from each side.

Answer: 105

ABC is an equilateral triangle. bisects

a. Find x.

Answer: 30

b.

Answer: 90

- Geometry:Pg. 219 #9 – 28, 36, 40
- Pre-AP Geometry:Pg. 219 #9 – 30, 35 – 37, & 40