Download Honors Geometry - Writing Proofs Assignment

Honors Geometry - Writing Proofs Assignment - ANSWERS
Choose 3 of the 4 problems below to do. For each problem, write a two -column proof
(statements/reasons).
1
..
C
A
B
E
1) AE // CD
D
1) Given
B is the midpoint of EC
2) EB = BC
2) Definition of midpoint
3) <A = <D (or <C = <E)
3) Alternate interior angles are congruent
4) <ABE = <DBC
4) Vertical angles are congruent
5) ∆ABE ≅ ∆DBC
5) AAS (if step 3 is <A = <D) OR
ASA (if step 3 is <E = <C)
T
2
..
R
S
M
L
1) TL and RM bisect each other
1) Given
2) TS = SL
2) definition of bisector
RS = SM
3) <RST = <MSL
3) Vertical angles are congruent
4) ∆RST = ∆MSL
4) SAS
5) <T ≅ <L
5) CPCTC
G
3
..
H
1)
∆HGK is isosceles (GH ≅ GK)
J
K
1) Given
J is the midpoint of HK
2)
3)
4)
5)
HJ = JK
GJ = GJ
∆HGJ = ∆KGJ
<HGJ = <KGJ
2) definition of midpoint
3) reflexive property
4) SSS
5) CPCTC
**Note: Students could use <H = <K by the Isosceles theorem and then the triangles would be
congruent by SAS.
Prove: <HGJ ≅ <KGJ
L
4
..
E
1)
2)
3)
4)
5)
6)
LN is the perpendicular bisector of EO
EN = NO
<LNE and <LNO are right angles
<LNE = <LNO
LN = LN
∆LNE = ∆LNO
N
O
1) Given
2) definition of bisector
3) definition of perpendicular
4) Right angles are congruent.
5) reflexive property
6) SAS