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Aim:. K. Given:. C. A. B. Prove:. What theorems apply to isosceles and equilateral triangles?. Do Now:. Given. Given. Def. angle bisector. Reflexive Postulate. S.A.S. Postulate . C.P.C.T.C. Isosceles Triangle Theorem:. T. E. P. ). Z. ). ). ). G. ). ). D. Q. V. M. ).

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Aim:

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### Aim:

K

Given:

C

A

B

Prove:

What theorems apply to isosceles and equilateral triangles?

Do Now:

Given

Given

Def. angle bisector

Reflexive Postulate

S.A.S. Postulate

C.P.C.T.C.

Geometry Lesson: Isosceles and Equilateral Triangle Theorems

### Isosceles Triangle Theorem:

T

E

P

)

Z

)

)

)

G

)

)

D

Q

V

M

)

)

Theorem #8:

Base angles of an isosceles triangle are congruent.

Isosceles triangles

Corollary #8-1:

The bisector of the vertex angle of an isosceles triangle bisects the base.

Corollary #8-2:

x

The bisector of the vertex angle of an isosceles triangle is perpendicular to the base.

In other words:The median, altitude and angle bisector from the vertex of an isosceles triangle are all the same segment.

Geometry Lesson: Isosceles and Equilateral Triangle Theorems

B

B

B

Or

Or

)

)

)

)

)

)

A

C

A

C

A

C

B

)

)

)

C

### Equilateral Triangles

Corollary #8-3:

Every equilateral triangle is equiangular.

Geometry Lesson: Isosceles and Equilateral Triangle Theorems

L

Q

K

D

F

T

### Ex: Isosceles Triangles

If the following pairs of segments are congruent, which angles are congruent.

Geometry Lesson: Isosceles and Equilateral Triangle Theorems

V

Given:

A

T

K

R

M

Prove:

### Ex: Proof w/Isosceles Triangle

Given

Given

Def. Of midpoint

Given

A.S.A. Postulate

C.P.C.T.C

Geometry Lesson: Isosceles and Equilateral Triangle Theorems

1) Given:

Prove:

D

2) Given:

T

M

R

Prove:

V

y

x

A

3) Given:

G

D

H

T

Q

N

Prove:

L

E

P

### Proofs w/Isosceles Triangles

Geometry Lesson: Isosceles and Equilateral Triangle Theorems

### Algebra w/Isosceles Triangles

Geometry Lesson: Isosceles and Equilateral Triangle Theorems