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Brett Solberg AHS ‘11-’12. Isosceles and Equilateral Triangles. Warm-up. 1)What does CPCTC mean? Explain it in your own words. Unscramble the letters to reveal a type of triangle. 2) seicslose 3) telqariulae 4) giaqunearul Do you want to review any HW problems? . - PowerPoint PPT Presentation

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Isosceles and Equilateral Triangles Brett Solberg AHS ‘11-’12

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Isosceles and Equilateral Triangles

Brett Solberg AHS ‘11-’12

Warm-up

1) What does CPCTC mean? Explain it in your own words.

Unscramble the letters to reveal a type of triangle.

2) seicslose

3) telqariulae

4) giaqunearul

Do you want to review any HW problems?

Isosceles Triangles A triangle where exactly 2

sides are congruent. Legs – the 2 congruent sides Vertex Angle – the angle

formed by the legs. Base – Third side of the

triangle. Base Angles – 2 angles

adjacent to the base.

Isosceles Triangles

Identify the legs, base, base angles, and vertex of the triangle.

Legs – Base – Base Angles – Vertex –

Isosceles Triangles

Identify the legs, base, base angles, and vertex of the triangle.

Legs – Base – Base Angles – Vertex –

Isosceles Triangles

Identify the legs, base, base angles, and vertex of the triangle.

Legs – Base – Base Angles – Vertex –

Isosceles Triangle Theorem If two sides of a triangle are

congruent, then the angles opposite them are congruent.

If AB ≅ AC, then ∠B ≅ ∠C

Example

Converse of Isosceles Triangle Thm If two angles of a triangle are

congruent, then the sides opposite them are congruent.

If ∠B ≅ ∠C then AB ≅ AC

Example

Example

Solve for y.

Example

Solve for x.

Example

Solver for x.

Vocab

Bisector

Perpendicular Bisector

A B

Theorem 4.5

The bisector of the vertex angle is the perpendicular bisector of the base.

Isosceles Review

Base Angles Theorem Converse

Transition

#3 - Corollary to the Base Angles Thm If a triangle is equilateral, then it is

equiangular.

Transition

#4 - Corollary to the Converse of the Base Angles Thm If a triangle is equiangular, than it is

equilateral.

Reflection

What is the measure of the angles of any equiangular triangle?

What is the measure of the angles of any equilateral triangle?

What does this symbol represent?

The Triforce

The Triforce

How many equilateral triangles are there in the trifoce?

Example

Find the value of x and y.

Example

Review

Review

If 2 sides of a triangle are congruent, than the angles opposite them are congruent.

If two angles are congruent, then the sides opposite them are congruent.

Review

If a triangle is equilateral, then it is equiangular.

If a triangle is equiangular, then it is equilateral.

The angles in any equilateral or equiangular triangle are 60°.

Homework

4.5 Worksheet and pg 230#1-13

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