2-3 Proving Theorems

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10 Οκτ 2013 (πριν από 3 χρόνια και 9 μήνες)

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MIDPOINT THEOREM

If M is the midpoint of AB, then
AM = ½ AB and MB = ½ AB.

A

M

B

Given: M is the midpoint of AB

Prove:
AM = ½ AB; MB = ½ AB

Statements

Reasons

1.

M is the midpoint of AB

1. Given

2. AM

= MB

2. Def. of
midpt
.

3. AM + MB = AB

3.
Seg
. Add. Post.

4. AM + AM = AB, or 2AM = AB

4. Substitution
(from steps 2 & 3)

5. AM = ½AB

5. Division Prop. =

6. MB = ½AB

6. Substitution

(from steps 2 & 5)

A

M

B

ANGLE BISECTOR THEOREM

If ray BX is the bisector of <ABC,
then m<ABX = ½ m<ABC and
m<XBC = ½ m<ABC.

B

A

X

C

Given:

ray BX is the bisector of <ABC

Prove: m<ABX = ½ m<ABC; m<XBC = ½ m<ABC

B

A

X

C

Statements

Reasons

1.

Ray BX is bisector of <ABC

1. Given

2. m<ABX = m<XBC

2. Def. of angle

bisector

3. m<ABX + m<XBC

= m<ABC

3. Angle Add. Post.

4. m<ABX + m<ABX

= m<ABC,
or 2(m<ABX) = m<ABC

4. Substitution

5. m<ABX = ½ m<ABC

5. Multiplication Prop. =

6. m<XBC = ½ m<ABC

6. Substitution

(from steps 2 & 5)

CLASSWORK

p. 45
CEx
. (1


9)


Prove the following:

Given: ray EG is the bisector of <DEF;


ray SW is the bisector of <RST;


m<DEG = m<RSW

Prove: m<DEF = m<RST

E

D

G

F

S

R

W

T

p. 46
WEx
. (1
-
8, 15
-
18)

HOMEWORK