Post on 16-Feb-2016
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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