Download Notes 4-5 - Robinson Schools

SB En Geom 4­5 Completed.notebook
October 03, 2012
Lesson 4­5 Isosceles and Equilateral Triangles
Isosceles triangles ­ triangle with at least two sides congruent
legs ­ the two congruent sides
base ­ the noncongruent side
Vertex
Angle
vertex angle ­ angle formed by the legs
base angles ­ angles opposite the legs
Leg
Leg
Base
Angle
Base
Angle
Base
Oct 7­8:28 AM
Thm 4­3 Isosceles Triangle Thm
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
then
If
Thm 4­4 Converse of Isosceles Triangle Thm
If two angles of a triangle are congruent, then the sides opposite the angles are congruent.
If
then
Thm 4­5
The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base.
Oct 7­8:32 AM
1
SB En Geom 4­5 Completed.notebook
October 03, 2012
X
Prove the Isosceles Triangle Thm.
12
Given: XY ≅ XZ, XB bisects <YXZ
Prove: <Y ≅ <Z
Y
Z
B
1. 1.
2. 2.
3. 3.
4. 4.
5. 5.
Oct 7­8:38 AM
Expl 1. Explain why each statement is true.
T
a. <WVS ≅ <S
U
b. TR ≅ TS
W
R
V
S
Ckpt 1. Can you deduce that ΔRUV is isosceles? Explain.
Oct 7­8:41 AM
2
SB En Geom 4­5 Completed.notebook
October 03, 2012
Expl 3. Find the value y.
M
y
a. 17 b. 27
c. 54 d. 90
N
63
O
L
Ckpt 2. Suppose m<L = 43. Find the values of y.
Oct 7­8:45 AM
corollary ­ a statement that follows immediately from a theorem
Corollary to Thm. 4­3
If a triangle is equilateral, then it is equiangular.
If, then
Corollary to Thm 4­4
If a triangle is equiangular, then it is equilateral.
If, then
Oct 7­8:49 AM
3
SB En Geom 4­5 Completed.notebook
October 03, 2012
Expl 3. Find x.
X
Ckpt 3. What is the measure of the angle at each outside corner of the path?
Oct 7­8:53 AM
Homework
Lesson 4-5
1-32
Oct 7­8:57 AM
4