moomoomath logo header
lime green horizontal line
Welcome to MooMooMath
study skills A teachers secret guide to your best grades
Master the 7 pillars of school success

Improve your grades and lower your stress
A-Z Video List
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


side measure isosceles triangle
black line
black line

How to prove a Triangle is Isosceles

Isosceles Triangle Theorems

two equal sides triangle
isosceles triangle
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
right triangle with angles of 50 40 90
40
​50
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. 






isosceles triangle with leg leg base/isosceles triangle theorem
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
isosceles triangle
C
B
A
perimeter formula isosceles triangle
h
measure angle isosceles triangle
black line
​AB ≌AC
then
≮B ≌ ≮C
​≮ B ≌ ≮ C
then

AB ≌AC
congruent sides triangle/isosceles triangle theorem
triangle with congruent angles
​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
base of triangle/#isosceles triangle
altitude of triangle
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
isosceles triangle picture #isosceles triangle
__
__
__
__
DB ≌ DC
__
__
b
c
a
vertex angle isosceles triangle
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

Isosceles triangle theorems