Which is the correct definition of isosceles a a triangle with at least 2 congruent sides b a triangle with exactly 2 congruent sides 45 Isosceles Triangles LEQ How can we use properties of isosceles triangles to construct proofs ID: 323352
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Slide1
Warmup
Which is the correct definition of isosceles?
a.) a triangle with at least 2 congruent sides
b.) a triangle with exactly 2 congruent sidesSlide2
4.5 Isosceles Triangles
LEQ: How can we use properties of isosceles triangles to construct proofs?Slide3
Word Bank
Leg
Leg
Vertex
Base
Base AnglesSlide4
Given ABC is isosceles. Prove m<A=m<B.
Proof:
1.) Definition of Isosceles
2.)
Defn
. of bisect
1.) AC=BC
*Construct CD so that it bisects <C*
2.)m<ACD=m<BCD
3.) CD=CD
3.) reflexive property
4.) ACD
BCD
4.) SAS
What can you conclude about <A and <B?
5.) <A <B
Statements
Reasons
5.) CPCTC
A
B
C
DSlide5
Isosceles Triangle Theorem:
If 2 sides of a triangle are congruent, then the base angles are congruent as well.
Converse:
If the base angles of a triangle are congruent, then the 2 opposite legs of the triangle are congruent as well.
What kind of statement is this?Slide6
Given BC=AC, answer the following:
a.) If m<1=140, m<2=_____,
m<3=______ and m<4=______
b.) If m<4=65, m<2=_____,
m<3=______and
m<1=______.
A
1
2
3
4
B
CSlide7
Corollaries (small theorem that follow a big theorem)
An equilateral triangle is also equiangular.
An equiangular triangle has all 60 angles.Slide8
Perpendicular bisector:
Draw an isosceles triangle
Bisect
the
vertex
What do you notice about the
intersection of the bisector
and the base?Slide9
Corollary 3
The bisector of the vertex of an isosceles triangle is a perpendicular bisector of the base.
(divides the base in half and is perpendicular to the base)Slide10
Try examples 1-3.Slide11
Ex. 1
An exterior angle of an isosceles triangle has the measure 11o degrees. What are the 2 possible sets of measures for the angles of the triangle?
110
110
70
70
40
110
70
70+x+x=180
x=55
40,70,70 and 70,55,55
x
xSlide12
Ex. 2: Find the values of m and n:
45
m
n
60
m=
m+n
=