1. Warmup
Which is the correct definition of isosceles? a.) a triangle with at least 2 congruent sides b.) a triangle with exactly 2 congruent sides

2. 4.5 Isosceles Triangles
LEQ: How can we use properties of isosceles triangles to construct proofs?

3. Word Bank
Leg
Vertex
Base
Base Angles

4. Given ABC is isosceles. Prove m<A=m<B. Proof:
Statements
Reasons
1.) AC=BC
1.) Definition of Isosceles
*Construct CD so that it bisects <C*
2.)m<ACD=m<BCD
2.)Defn. of bisect
3.) CD=CD
3.) reflexive property
4.) ACD BCD
4.) SAS A
What can you conclude about <A and <B? D B
5.) <A <B
5.) CPCTC

5. 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?

6. Given BC=AC, answer the following: a
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=______. C 1 2 4 3 A B

7. Corollaries (small theorem that follow a big theorem)
An equilateral triangle is also equiangular.
An equiangular triangle has all 60 angles.

8. Perpendicular bisector:
Draw an isosceles triangle
Bisect the vertex
What do you notice about the
intersection of the bisector and
the base?

9. 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)

10. Try examples 1-3.

11. 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?
40,70,70 and 70,55,55
110
110 40 70
70+x+x=180
x=55 x
110 x 70 70

12. Ex. 2: Find the values of m and n:
m+n= 45 60 m= n m