4 7 use isosceles and equilateral triangles n.
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4.7 Use Isosceles and Equilateral Triangles. Define Isosceles . A triangle is isosceles iff it has two or more congruent sides (yes an equilateral triangle is also isosceles). Isosceles Triangle. vertex. Leg. Leg. base angle. base angle. Base. A. C. B.

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Presentation Transcript
define isosceles
Define Isosceles
  • A triangle is isosceles iff it has two or more congruent sides (yes an equilateral triangle is also isosceles)
isosceles triangle
Isosceles Triangle

vertex

Leg

Leg

base angle

base angle

Base

isosceles triangle theorem base angles theorem

A

C

B

Isosceles Triangle Theorem (Base Angles Theorem)
  • If two sides of a triangle are congruent (isosceles triangle), then the angles opposite them are congruent
slide5

K

J

M

L

2. Draw JM

3. MK = ML

~

4. JK = JL

~

5. JM = JM

~

6. JMK = JML

~

7. < K = <L

~

Given: JK = JL

Prove <K = <L

~

R

S

1. Definition of a midpoint

1. Define M as the midpoint of the base

2. Two points determines a line

~

3. Definition of a midpoint

4. Given

5. Reflexive Property

6. SSS

7. CPCTC

converse of the isosceles triangle theorem converse of the base angles theorem

A

C

B

Converse of the Isosceles Triangle Theorem (Converse of the Base Angles Theorem)
  • If two angles of a triangle are congruent, then the sides opposite them are congruent
corollaries
Corollaries
  • If a triangle is equilateral, then it is equiangular
  • If a triangle is equiangular, then it is equilateral
  • If a triangle is equilateral (and equiangular) then it is a regular triangle
  • If a triangle is equilateral (and equiangular) then the angles are 60°
homework
Homework
  • Page 267/1, 2, 4-6, 8-10, 12-14, 19, 26-29, 35, 36, 52, 54, 56