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Common Core Standard: 6.GA.1   6th Grade Math

## Which of these triangles would be isosceles?

Related Sites covering Isosceles Triangles

Practice with Isosceles Triangles/Regents  Use this link as a quick review of Isosceles triangles by solving the practice problems dealing with Isosceles Triangles on this page.

Theorems about Isosceles Triangles/Dr. Wilson  Definition and key points of the Isosceles Triangle Theorem   # Isosceles Triangle Theorems  Two equal angles and sides so it is an isosceles triangle
Two equal angles and sides so it is an  isosceles triangle
Three different angle measures and three unequal sides so it is not an isosceles triangle 40
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The Perimeter formula of an Isosceles Triangles = 2a + b

a =legs
b = base

Area Formula = 1/2 base x height
In order to be classified as an isosceles a triangle it must have two equal legs  and two equal angles Leg
Leg
Base
A
B
C
Measure Angle of IsoscelesTriangle ABC equals
Side Length of Isosceles Triangle ABC equals
a= length of legs
b= length of base
h= Altitude C
B
A h  ​AB ≌AC
then
≮B ≌ ≮C
​≮ B ≌ ≮ C
then

AB ≌AC  ​Theorem: If two sides of a triangle are congruent, then the angles opposite the sides are congruent
Theorem: If two angles of a triangle are congruent, then the sides opposite the angles are congruent  The altitude to the base of an isosceles triangle bisects the vertex angle.

The altitude to the base of an isosceles triangle bisects the base.

​D
​D
≮DAB ≌ ≮DAC __
__
__
__
DB ≌ DC
__
__
b
c
a Vertex angle of an isosceles triangle is the non congruent angle in an isosceles triangle.                                                                                                                                                                                 The vertex angle is always opposite the base.

​The base angles are the angles that are opposite the pair of equal sides of the triangle. (<C and < B)

C
B
A
Base Angles
Given a vertex angle of 110 °, what is the measure of your base angles?

Step 1. The interior measure of a triangle equals 180 therefore 180-110 =70

Step 2. Each base angle is opposite a congruent side and therefore are congruent.
As a result, 70÷2 = 35 ° which equals the measure of each base angle

What is the measure of your vertex given a base angle of 70°?

Step 1 Each base angle is congruent therefore, 70 x2 = 140

Step 2. Interior angle measure triangle = 180 therefore 180 -140 = 40°

The altitude of an isosceles triangles forms two congruent triangles
Vertex angle of an isosceles triangle