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Geometry Lesson 4­5 Isosceles and Equilateral Triangles.notebook
September 19, 2012
Section 4­5 Isosceles and Equilateral Triangles
Review: B
1. Name the angle opposite AB.
2. Name the angle opposite BC.
A
75
x
30
C
3. Name the side opposite < A.
4. Name the side opposite < C.
5. Find the value of x.
Oct 8­1:45 PM
Basic Information:
Legs
Base
Base Angles
Oct 8­1:50 PM
1
Geometry Lesson 4­5 Isosceles and Equilateral Triangles.notebook
September 19, 2012
What is the difference between an isosceles triangle and an equilateral triangle?
Can an isosceles triangle be an equilateral triangle?
Can an equilateral triangle be an isosceles triangle?
Oct 8­2:00 PM
Theorem 4­3: Isosceles Triangle Theorem ­ If two sides of a triangle are congruent, then the angles opposite those sides are congruent. C
< A ≅ < B
A
B
Theorem 4­4: Converse of Isosceles Triangle Theorem ­ If two angles of a triangle are congruent, then the sides opposite the angles are congruent.
C
AC ≅ BC
A
B
Oct 8­1:52 PM
2
Geometry Lesson 4­5 Isosceles and Equilateral Triangles.notebook
September 19, 2012
Theorem 4­5 : The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base.
C
CD AB and CD bisects AB
A
B
D
Oct 8­1:58 PM
Example 1)
Proving the Isosceles Triangle Theorem
X
12
Given: XY ≅ XZ, XB bisects < YXZ
Prove: < Y ≅ < Z
Y
B
Z
Oct 8­2:01 PM
3
Geometry Lesson 4­5 Isosceles and Equilateral Triangles.notebook
September 19, 2012
T
Example 2)
Explain why RST is isosceles.
U
W
R
S
V
Can we conclude that RUV is isosceles?
Oct 8­2:08 PM
M
Example 3)
Find the values of x and y
y
N
x
63o
O
L
Now, suppose < L = 43. Find the values of x and y.
Oct 8­2:09 PM
4
Geometry Lesson 4­5 Isosceles and Equilateral Triangles.notebook
September 19, 2012
[A corollary is a statement that follows immediately from a theorem. ]
Corollary to Theorem 4­3 : If a triangle is equilateral, then the triangle is equiangular.
Y
< X ≅ < Y ≅ < Z
Z
X
Corollary to Theorem 4­4 : If a triangle is equiangular, then the triangle is equilateral. Y
XY ≅ YZ ≅ ZX
X
Z
Oct 8­2:09 PM
Example 4)
Find x given that the rectangles have angles measuring 90 o and that the triangles are equiangular.
x
Oct 8­2:15 PM
5
Geometry Lesson 4­5 Isosceles and Equilateral Triangles.notebook
September 19, 2012
Sep 19­8:48 AM
6
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