Download Recognizing Sets of Steps in Proofs December 13, 2010

December 13, 2010
Recognizing
Sets of Steps
in Proofs
December 13, 2010
Perpendicular Lines:
3 steps
1. AB ⊥ CD
1. Given
2. <ABC and <ABD
are right angles
2. Definition of
perpendicular lines
3. <ABC ≅ <ABD
A
3. All right angles are
congruent.
December 13, 2010
Bisectors: 2 steps
(A bisector can divide an angle or
a line segment. Look carefully!)
1. BA bisects <CBD
3. <ABC ≅ <ABD
1. Given
A/S
3. Definition of a
bisector.
December 13, 2010
Midpoint: 2 steps
*A segment bisectors and a midpoint BOTH
divide a segment into two congruent segments --but don’t say one name instead of the other!
1. D is the midpoint
of BC.
3. BD ≅ CD
1. Given
S
3. Definition of a
midpoint.
December 13, 2010
Supplementary Angles:
4 steps
(Look for an extended straight line.)
S U P
1
2
3
P
4
1. straight line (ABCD)
1. Given
2. <1 ≅ <2
2. Given
3. <1 and <3 are
supplementary;
<2 and <4 are
supplementary
3. Linear pairs form
supplementary angles.
4. <3 ≅ <4
A
4. If two angles are
congruent, their
supplements are
congruent.
December 13, 2010
Every "Given" should lead to a pair
of congruent sides or angles!!
December 13, 2010
D
2
E
Given: <1 = <2
DB bisects AE at C
Prove: ∆ABC ≅ ∆EDC
4
3
A
1
C
B
December 13, 2010
A
Given: AC bisects <BAD
AB ≅ AD
1 2
Prove: ∆ABC ≅ ∆ADC
B
C
D