proof packet - Mary Star of the Sea High School

GEOMETRY NOTES
4.6 THE PROOFS HAVE ARRIVED!!!
NAME____________
What do I already know? What can I use to write a proof?
DEFINITIONS
MIDPOINT
ANGLE BISECTOR
VERTICAL ANGLES
SEGMENT BISECTOR
LINEAR PAIR
PERPENDICULAR
SUPPLEMENTARY
RIGHT TRIANGLE
COMPLEMENTARY
ISOSCELES TRIANGLE
EQUILATERAL TRIANGLE
POSTULATES AND THEOREMS
SEGMENT ADDITION
ANGLE ADDITION
PARALLEL LINES
ALTERNATE INTERIOR ANGLES
CORRESPONDING ANGLES
ALTERNATE EXTERIOR ANGLES
CONSECUTIVE INTERIOR ANGLES
TRIANGLES
AAS
3RD ANGLE
ASA
EXTERIOR ANGLES
SAS
TRIANGLE SUM
SSS
CPCTC
HL
ALGEBRAIC PROPERTIES
REFLEXIVE
SUBSTITUTION
How do I write a proof?
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Organize your thoughts.
Make a plan before you write.
Be sure to justify each step with an appropriate reason.
SSS ≅ Proofs:
1.
GIVEN:
Statements
Reasons
Statements
Reasons
Statements
Reasons
Statements
Reasons
AB ! CD
BC ! DA
PROVE:
ΔABC ≅ ΔCDA
2.
GIVEN: AB ! BC
D is the midpt of AC
PROVE: ΔABD ≅ ΔCBD
SAS ≅ Proofs:
3.
GIVEN:
AB ll CD , AB ! CD
PROVE:
ΔABC ≅ ΔDCB
4.
GIVEN: B is the midpoint of
AE and CD
PROVE: ΔABD ≅ ΔEBC
HL ≅ Proofs:
5.
Statements
Reasons
Statements
Reasons
Statements
Reasons
Statements
Reasons
GIVEN: ON ! MN , ON ! OP ,
MO ! NP
PROVE: ΔNPO ≅ ΔOMN
6.
GIVEN: PS ! RS , QR ! RS ,
QS ! PR
PROVE: ΔPRS ≅ ΔQSR
ASA ≅ Proofs:
7.
GIVEN: LN ll MO , LMll NO
PROVE: ΔONM ≅ ΔLMN
8.
GIVEN: WU ll YV , XU ll ZV ,
WX ! YZ
PROVE: ΔWXU ≅ ΔYZV
AAS ≅ Proofs:
9.
Statements
Reasons
Statements
Reasons
GIVEN: GF bisects ∠HGJ, ∠H ≅ ∠J
PROVE: ΔGFH ≅ ΔGFJ
10.
GIVEN: ∠B ≅ ∠D, !DAE " !BEA
PROVE: ΔABC ≅ ΔEDC
Do you accept the Extra Challenge Proof?
11.
GIVEN: ∠R ≅ ∠S, ∠2 ≅ ∠3
PROVE: RU ! SU
Statements
Reasons
MIXED PROOFS:
12.
Statements
Reasons
Statements
Reasons
Statements
Reasons
GIVEN: QT ! RS
QT / /RS
PROVE: !QRT " !STR
R
S
Q
T
13.
GIVEN: ZW ll UV
I is the midpt. of ZV
PROVE: ∆ZWI ≅ ∆VUI
U
Z
I
W
V
14.
GIVEN: HI ! KI , GK ! HG
HK bisects ∠IHG
PROVE: ∆HIK ≅ ∆HGK
15.
GIVEN: FP // LM, FL // MP
Statements
Reasons
Statements
Reasons
Statements
Reasons
PROVE: FP ≅ LM
L
F
1
P
4
2
3
M
P
16.
GIVEN: B is the midpt. of
DE and !A " !C
PROVE: B is the midpt. of
AC .
E
A
B
C
D
17.
GIVEN: PG ! GK , ∠3 ≅ ∠1
PROVE: GL bisects !ALK
G
P 4
3
1
5 6
L
2 K
18.
GIVEN: E is the midpt. of
Statements
Reasons
Statements
Reasons
Statements
Reasons
AD and BC
PROVE: AC // BD
B
A
E
D
C
19.
GIVEN: RK ll IH , RS ≅ SH
PROVE: IS ≅ KS
20.
GIVEN: M is the midpt. of AB
∠1 ≅ ∠2, ∠3 ≅ ∠4
PROVE: ∆AMC ≅ ∆BMD
D
C
A
1
3
M
4
2
B
21.
GIVEN: ∠1 ≅ ∠2, ∠3 ≅ ∠4
Statements
Reasons
Statements
Reasons
Statements
Reasons
PROVE: ∆QTV ≅ ∆SVT
Q
S
1
T
2
3
4
V
22.
GIVEN: XW bisects TV
∠T and ∠ V are rt.∠s
TQ ! VS
PROVE: ∆TWQ ≅ ∆VWS
T
Q
W
V
X
S
23.
GIVEN: MO ! PO
NO bi sects MP
PROVE: !MNO " !PNO
24.
Statements
Reasons
Statements
Reasons
Statements
Reasons
GIVEN: HK ! GI , HG ! IK
PROVE: ∠G ≅ ∠K
I
H
G
K
25.
GIVEN: AB ! BC , BD ! AC
DB bisects AC
PROVE: !ABC is isosceles
A
D
C
B
26.
GIVEN: EH ! GK , ∠E ≅ ∠G
PROVE: FH ! FK
27.
GIVEN: ∠A ≅ ∠D
Statements
Reasons
Statements
Reasons
Statements
Reasons
C is the midpoint of AD
PROVE: ∠ABC ≅ ∠DBC
28.
GIVEN: AB ! BC
AD ! DC
CA bi sects !DAB
PROVE: !ACB " !ACD
29.
GIVEN: BC ! AD , AC ! BD
PROVE: ∠BAD ≅ ∠ABC
30.
Statements
Reasons
Statements
Reasons
Statements
Reasons
GIVEN: RU ||VS
T is the midpoint of SU
PROVE: RT ! VT
31.
GIVEN:
EB bi sects !AEC
and !1 " !5
PROVE: AB ! BC
32.
GIVEN:
PR bi sects !TPS
and !TRS
PROVE: !TQR " !SQR

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