Name
T E K S G.1.A
Date
Practice
LESSON
2-6
Geometric Proof
Write a justification for each step.
_
Given: AB = EF, B is the midpoint
_of AC ,
and E is the midpoint of DF .
_
&
%
$
!
"
1. B is the midpoint of AC , _
and E is the midpoint of DF .
_
_
Class
_
#
Given
_
2. AB BC , and DE EF .
Def. of mdpt.
3. AB BC, and DE EF.
Def. of ⬵ segments
Seg. Add. Post.
4. AB BC AC, and DE EF DF.
5. 2AB AC, and 2EF DF.
Subst.
6. AB EF
Given
7. 2AB 2EF
Mult. Prop. of 8. AC DF
Subst. Prop. of _
_
Def. of ⬵ segments
9. AC DF
Fill in the blanks to complete the two-column proof.
10. Given: HKJ
is a straight angle.
__›
KI bisects HKJ.
Prove: IKJ is a right angle.
(
+
*
)
Proof:
Statements
1. a.
⬔HKJ is a straight angle.
2. mHKJ 180
__›
3. c.
KI bisects ⬔HKJ
Reasons
1. Given
2. b.
Def. of straight ⬔
3. Given
4. IKJ IKH
4. Def. of bisector
5. mIKJ mIKH
5. Def. of 6. d.
m⬔IKJ m⬔IKH m⬔HKJ
6. Add. Post.
7. 2mIKJ 180
7. e. Subst. (Steps
8. mIKJ 90
8. Div. Prop. of 9. IKJ is a right angle.
9. f.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
13
2, 5, 6
)
Def. of right ⬔
Holt Geometry
Name
T E K S G.1.A
Date
Practice
LESSON
2-6
Geometric Proof
Write a justification for each step.
_
Given: AB = EF, B is the midpoint
_of AC ,
and E is the midpoint of DF .
_
&
%
$
!
"
1. B is the midpoint of AC , _
and E is the midpoint of DF .
_
_
Class
_
#
Given
_
2. AB BC , and DE EF .
Def. of mdpt.
3. AB BC, and DE EF.
Def. of ⬵ segments
Seg. Add. Post.
4. AB BC AC, and DE EF DF.
5. 2AB AC, and 2EF DF.
Subst.
6. AB EF
Given
7. 2AB 2EF
Mult. Prop. of 8. AC DF
Subst. Prop. of _
_
Def. of ⬵ segments
9. AC DF
Fill in the blanks to complete the two-column proof.
10. Given: HKJ
is a straight angle.
__›
KI bisects HKJ.
Prove: IKJ is a right angle.
(
+
*
)
Proof:
Statements
1. a.
⬔HKJ is a straight angle.
2. mHKJ 180
__›
3. c.
KI bisects ⬔HKJ
Reasons
1. Given
2. b.
Def. of straight ⬔
3. Given
4. IKJ IKH
4. Def. of bisector
5. mIKJ mIKH
5. Def. of 6. d.
m⬔IKJ m⬔IKH m⬔HKJ
6. Add. Post.
7. 2mIKJ 180
7. e. Subst. (Steps
8. mIKJ 90
8. Div. Prop. of 9. IKJ is a right angle.
9. f.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
13
2, 5, 6
)
Def. of right ⬔
Holt Geometry