USE ISOSCELES AND
EQUILATERAL TRIANGLES
CH 4.7
In this section…
 We will use the facts that we know about isosceles
and equilateral triangles to solve for missing sides
or angles.
What do you know about an isosceles
triangle?
 There are two congruent sides in an
isosceles triangle and two congruent
angles.
What do you remember about an equilateral
triangle?
 All of the sides and angles should be
congruent.
 The angles in an equilateral triangle
always equal 60o.
Base Angles Theorem
 If two sides of a triangle are congruent, then the
base angles are also congruent.
 Base angles are the angles at the ends of the 2
congruent segments.
 So, in the diagram angles B and C are congruent.
Base angle
Base angle
Converse to the Base Angles Theorem
 If two angles in a triangle are congruent, then the
triangle is an isosceles triangle.
 That means that the 2 sides of the triangles are
also congruent.
Find the value of x.
This is an isosceles
triangle, so the 2 sides
are congruent…
5x + 5 = 35
5x = 30
x =6
This is an isosceles
triangle, so the 2 angles are
congruent…
9x = 72
x=8
x + x + 102 = 180
2x + 102 = 180
2x = 78
x = 39
The sum of the
interior angles is
180…
55 + 55 + y = 180
110 + y = 180
y = 170
x + 7 = 55
x = 48
If this is an isosceles
triangle then what are the
two congruent angles
x = 45
9y = 45
y=5
How would you find the values of x and y?
What are all of the missing angles?
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