Download Use isosceles and equilateral triangles

USE ISOSCELES AND
EQUILATERAL TRIANGLES
Lesson 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.
 You know that a triangle is isosceles if it has at
least two congruent sides. When an isosceles
triangle has EXACTLY two congruent sides, these
two sides are the legs. The angle formed by the
legs is the vertex angle. The third side is the base
of the isosceles triangle. The angles adjacent to
the base are called base 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.
Theorem 4.7: 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
Theorem 4.8:
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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