TEQ – Typical Exam Questions

J

Q

P

M

K

L

O

Given: JKLM is a parallelogram OLJO

OQOP Prove:

Statement Reason

2. Given

1. Given1. JKLM is a parallelogram

OLJO .2

21 .4

3. Opposite sides of a parallelogram are parallel

.3 MQLJPK

LOQJOP ΔΔ .6 ASAASA .6

.7 OQOP

43 .5

4. Parallel lines cut by a transversal form congruent alternate interior angles

5. Vertical angles are congruent

1

2

3

4

7. CPCTC

TEQ #1

DABC

BLDJ

ALCJ

Given: Parallelogram DEBK,

,

Prove:

C

J

L

D

B

K

E

A

Statement Reason1. Parallelogram

DEBK

DABC 2.

BLDJ .3

1. Given

2. Given

3. Given

5. Addition postulateJLBLJLDJ 5.

JBJLBL

DLJLDJ

6. 6. Partition postulate

JBDL 7. 7. Substitution postulate

4. Reflexive postulateJLJL 4.

.8 DKEB 8. Opposite sides of a parallelogram are parallel

21 .9 9. Parallel lines cut by a transversal form congruent alternate interior angles.

ΔALDJBΔ .10 C SASSAS .10

ALCJ 11. 11. CPCTC

Statement Reason

2. Given

3. Given

TEQ #3

6. Opposite sides of a parallelogram are both parallel and congruent

ACDF 2.

1. Given1. ABCD is a parallelogram

ABDCABDC and .6

ACEB 3.

anglesright

are 2 and 1 .4 4. Perpendicular segments form right angles

21 .5 5. All right angles are congruent

43 .7 7. Parallel lines cut by a transversal form congruent alternate interior angles

BEADFC ΔΔ .8 AASAAS .8

A

D C

B

1 2

4

3E

F

ACDF

Given: Parallelogram ABCD,

Prove: BEDF BEDF .9 CPCTC .9

Statement Reason

S

P Q

QRQ

PQRS amarallelogr :Given

P

P

2 to

congruentnot is 1 :Prove

PQRS amarallelogr 1. P 1. Given

TEQ #4

R QRQ 2. P 2. Given

21

3. 3. Assumption

4. PQRS is a rhombus 4. A parallelogram whose diagonal bisects an angle isa rhombus

5. 5. All sides of a rhombus are congruent

6.

6. Contradiction 2,5

Statement ReasonTEQ #5

2. Given

1. Given1. Rhombus ABCD

.3 EFDE 3. A midpoint divides a segment into two congruent parts

21 .4 4. Vertical angles are congruent

FEBDEC ΔΔ .7 ASAASA .7

.8 BFDC 8. CPCTC

43 .6 6. Parallel lines cut by a transversal form congruent alternate interior angles.

2. E is the midpoint of

.5 ABFDC 5. Opposite sides of a rhombus are parallel

.9 DADC 9. All sides of a rhombus are congruent

.10 BFAD 10. Substitution postulate

1

2

3

4

Statement Reason

TEQ #6

2. Given

1. Given1. ABDE is a parallelogram

DCAE .2

3. Opposite sides of a parallelogram are congruent

BDAE .3

4. Substitution postulateBDDC .4

5. A triangle with two congruent sides is isosceles

isosceles is .5 DBC

isosceles is :Prove DBC

Given: ABDE is a parallelogram

DCAE

Statement Reason

TEQ #7

2. Given

1. Given

2 1 .2

.3 ECAE 3. A segment bisector divides a segment into two congruent parts

7. Two lines cut by a transversal that form congruent alternate interior angles are parallel

.7 BCAD

CEBAED ΔΔ .5 ASAASA .5

.6 BCDA 6. CPCTC

A

D C

B

2

13

E

43 .4 4. Vertical angles are congruent

4

AC DB bisects .1

8. A quadrilateral that has one pair of opposite sides both parallel and congruent is a parallelogram

ramparallelog a is .8 ABCD

Statement Reason

TEQ #9

2. Given

1. Given

BEBD .2

3. AssumptionCA .3

4. Reflexive postulateBB .4

6. CPCTC

CBDABE .5

BCAB .1

ASA ASA .5

BEBD .6

CA .7 7. Contradiction 2,6

Statement Reason

TEQ #10

3. Opposite sides of a parallelogram are congruent

1. Given1. ABCD is a parallelogram

CBDA .3

CA .4 4. Opposite angles of a parallelogram are congruent

BCFDAE ΔΔ .5 SASSAS .5

Prove:

D

E

F

A

C

B

BCFDAE ΔΔ

Given: ABCD is a parallelogram

FCAE

2. GivenFCAE .2

Statement Reason

2. Given

1. Given1. ABCD is a parallelogram

.2 ACDE

BFCDEA ΔΔ .8 AASAAS .8

43 .7 7. Parallel lines cut by a transversal form congruent alternate interior angles

A

D C

B

12

4

3F

3. Given

anglesright

are 2 and 1 .4 4. Perpendicular segments form right angles

21 .5 5. All right angles are congruent

.9 FCAE 9. CPCTC

6. Opposite sides of a parallelogram are both congruent and parallel.

EACBF 3.

CBDACBDA , .6

FCAE :Prove

Statement Reason

S

P Q

Tat intersect RSand PQ

RS PQ:Given

RQand PSof

midpoint not the is T :Prove

RS PQ1. 1. Given

TEQ #8

R

Tat intersect RSand PQ2. 2. Given

3. PS and RQ

3. Assumption

4. 4. A midpoint divides a segment into two congruent parts.

5. 5. Vertical angles are congruent

6. 6.

T

7. 7. CPCTC8. 8. Contradiction 1,7