Download Isosceles Triangles 4-3A - Winterrowd-math

Isosceles Triangles
4-3A
What makes an isosceles unique?
What is an auxiliary line?
Isosceles Triangles
Parts
vertex
Vertex angle
leg
leg
Base angles
base
The Isosceles Have It!
An isosceles triangle has been drawn
on a piece of paper and then cut out.
(How do you draw an isosceles
triangle on a piece of paper?)
If the triangle is folded in half, what can
be said about the base angles?
What can be said about the sides?
Try It
In isosceles triangle ABC , AB  BC .
O
What else must be true?
In MNO, M  N . Find the
3x+8
4x−10
lengths of sides MO and NO.
M
N
Isosceles Triangle Theorem
If two side of a triangle are congruent, then the
angles opposite those sides are congruent.
Converse of the Isosceles
Triangle Theorem
If two angles of a triangle are congruent, then
the sides opposite those angles are congruent.
Unique Bisector Theorems
• Every segment has a unique midpoint.
• Every angle has a unique ray that bisects it.
Auxiliary Line
The auxiliary lights came on when the power went
out.
The ladies auxiliary made blankets for the homeless
shelter.
Auxiliary line is a line (or part of a line) added to a
figure.
You can add lines and points to a figure as long as
you can show that they actually exist.
Z
Proof
Given : In XYZ , XZ  YZ
Prove : X  Y
Statements
X
Reasons
Y
M
1. Draw M , the midpoint of XY
1.Every Segment has unique midpt
2. Draw ZM
2.Two pts determine line
3. XM  MY
4. ZM  ZM
5. XZ  YZ
6. XMZ  YMZ
7. X  Y
3. Def of midpt
4. Reflexive
5. Given
6. SSS
7. CPCTC
What makes an isosceles unique?
An isosceles triangle has two congruent
sides and two congruent base angles.
What is an auxiliary line?
Auxiliary line is a line (or part of a line) added
to a figure.
Assignment 4-3A
Page 289, 1-9,
13, 21-24