Download Section 4.3 Isosceles and Equilateral Triangles

Section 4.3 Isosceles and
Equilateral Triangles
Objective
• SWBAT use properties of isosceles and
equilateral triangles to find angle measures
and side lengths
Isosceles Triangles
The congruent sides of an isosceles
triangle are called legs
The other side is called the base
The two angles at the base are
called the base angles
Base Angles Theorem
If two sides of a triangle are congruent,
then the angles opposite of them are congruent
Symbols:
If 𝐴𝐵 ≅ 𝐴𝐶, then <C ≅ <B
Base Angles Theorem
Find the value of the missing angle
x = 55°
x = 68°
x = 45°
Converse of the Base Angles Theorem
If two angles of a triangle are congruent, then the
sides opposite them are congruent.
Symbols: If <B ≅ <C, then 𝐴𝐶 ≅ 𝐴𝐵
Use the Converse of the Base Angles
Theorem
Find the value of x
By the Converse to the Base Angles Theorem
DE = DF
x + 3 = 12
- 3 -3
x=9
You Try
Find the value of y
y = 50°
y=9
y = 12
Equilateral Triangles
If a triangle is equilateral, then it is equiangular.
Symbols: If 𝐴𝐵 ≅ 𝐴𝐶 ≅ 𝐵𝐶 , then < 𝐴 ≅< 𝐵 ≅< 𝐶
If a triangle equiangular, then it is equilateral.
Symbols: If < 𝐴 ≅< 𝐵 ≅< 𝐶, then 𝐴𝐵 ≅ 𝐴𝐶 ≅ 𝐵𝐶
Equilateral Triangles
Find the length of each side of the equiangular triangle.
QR = QT by the equiangular theorem
3x = 2x + 10
-2x -2x
x =10
3(10) = 30
Equilateral Triangles
Find the value of x.
2y + 5 = 4y - 3 by the equilateral theorem
-2y
-2y
5 = 2y - 3
+3
+3
8 = 2y
__
__
2
2
y=4
You Try!
Find the value of y
y=7
y=5