Transcript 4.6 Isosceles, Equilateral, and Right Triangles

Objectives:
• Use properties of isosceles and
equilateral triangles
• Use properties of right triangles
Properties of Isosceles Triangles
vertex angle
• In lesson 4.1, you learned
that a triangle is an isosceles
if it has at least two
congruent sides.
B
• The two angles adjacent to
the base are the base
angles. The angle opposite
the base is the vertex angle.
leg
leg
base angles
A
base
C
Remember:
A
• An EQUILATERAL triangle is
a special type of isosceles
triangle.
B
C
Equilateral and Isosceles Triangles
a.
b.
Find the value of x
Find the value of y
3x = 180
X = 60
x°
y°
Ex. 2: Using Equilateral and
Isosceles Triangles
a.
b.
Find the value of x
Find the value of y
120° + 2y° = 180°
2y = 60
y = 30
x°
60°
y°
Using Properties of Right
Triangles
• You have learned four ways to prove that
triangles are congruent.
•
•
•
•
Side-Side-Side (SSS)
Side-Angle-Side (SAS)
Angle-Side-Angle (ASA)
Angle-Angle-Side (AAS)
Solve:
Solution:
Isosceles Triangle
X = 180-54-54
X=72
Solve:
Solution:
Two Isosceles Triangles
1. 90- 28 = 62
2. 180-62-62 = 56
3. X=56
Solve:
Solution:
Two Isosceles Triangles
1. 180 – 65-65 = 50
2. 180 – 50-50 = 80
3. X= 80
65
50
50
=80
50
Solve:
Solution:
1. 120 = 60+60
2. 60= 60 vertical
angles
3. X = 60
60
60
60
60
60
Try this one:
Solution:
12 = 2x -12
24 = 2x
X = 12
One More:
Solution:
1. 180-68-68 = 44
2. 90 - 44 = 46
3. 4x – 2 = 46
Solve for x
4x = 48
X = 12
44
68
Last One:
Solution:
1. 146 = 13x + 3
2. 143 = 13x
3. 11