Quadrilateral Proofs

Page 4-5

(a) One pair of opposite side both parallel and congruent(b) Both pairs of opposite sides congruent(c) Both pairs of opposite angles congruent(d) Both pairs of opposite sides parallel(e) Diagonals bisect each other

Pg. 4 #1

Statement Reason

2. Given

3. Given

Pg. 4 #2

21 3.

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

CDAB 2.

5. A quadrilateral with one pair of opposite sides that are both parallel and congruent is a parallelogram

1. Given1. ABCD is a quadrilateral

CDAB .4

5. ABCD is a parallelogram

A

D C

B

1

2

Statement Reason

2. Given

3. Given

Pg. 4 #3

43 3.

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

21 2.

5. A quadrilateral with both pairs of opposite sides parallel is a parallelogram

1. Given1. PQRS is a quadrilateral

SRPQ

RQSP

.4

5. PQRS is a parallelogram

Statement Reason

2. Given

Pg. 4 #5

MJLM 2.median a is 1. LM

5. A quadrilateral with diagonals that bisect each other is a parallelogram

1. Given

5. GJKL is a parallelogram

KGM ofmidpoint theis 3. 3. A median extends from a vertex of a triangle to the midpoint of the opposite side

MGKM 4. 4. A midpoint divides a segment into 2 congruent parts

Statement Reason

2. Given

3. Two adjacent angles that form a straight line are a linear pair

Pg. 4 #8

1 2. C

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

1 ary tosupplement is 2 1.

8. A quadrilateral with both pairs of opposite sides parallel is a parallelogram

1. Given

DCAB .7

8. ABCD is a parallelogram

pairlinear a are and 2 3. DAB

4. Linear pairs are supplementaryarysupplement

are and 2 4. DAB

DAB1 5. 5. Supplements of the same angle are congruent

6. Two lines cut by a transversal that form congruent corresponding angles are parallel

CBDA .6

Statement Reason

2. Given

3. Given

Pg. 4 #12

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

SQPE 2.

1. Given1. PQRS is a parallelogram

RQSP

RQSP

.6

SQRF 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

RFQPES ΔΔ .8 AASAAS .8 .9 QFSE 9. CPCTC

Statement Reason

3. All angles of a rectangle are congruent

4. Opposite sides of a rectangle are congruent

Pg. 5 #1

CBDA 4.

5. A midpoint divides a segment into two congruent parts

BA 3.

1. Given1. ABCD is a rectangle

MBAM .5

MBCMAD .6 SASSAS .6 7. CPCTCCMDM .7

2. GivenABM ofmidpoint theis 2.

Statement Reason

2. Opposite sides of a rectangle are congruent

4. All angles of a rectangle are congruent

Pg. 5 #2

ABCDAB 4.

CBDA 2.

1. Given1. ABCD is a rectangle

CBADAB .5 SASSAS .5

6. CPCTC21 .6

ABAB 3. 3. Reflexive postulate

7. A triangle with two congruent base angles is isosceles

isosceles is .7 AEB

Statement Reason

2. Given

3. All sides of a rhombus are congruent

Pg. 5 #3

DCAD 3.

4. Reflexive postulate

CEAE 2.

1. Given1. ABCD is a rhombus

DEDE .4

CDEADE .5 SSSSSS .5

6. CPCTCCDEADE .6

Statement Reason

2. Given

3. All sides of a rhombus are congruent

Pg. 5 #4

CEAE 3.

4. Vertical angles are congruent

DCBFAB 2.1. Given1. AECB is a rhombus

21 .4

DCEFAE .9 ASAASA .9 10. CPCTCDEFE .10

43 .5 5. Opposite angles of a rhombus are congruent

6. Subtraction postulate43 6. DCBFAB

DCEDCBFAEFAB

43 7. 7. Partition postulate

FAEDCE 8. 8. Substitution postulate

Statement Reason

2. Given

3. Base angles of an isosceles trapezoid are congruent

Pg. 5 #8

CBADAB 3.ABDC // 2.

1. Given1. ABCD is an isosceles trapezoid

4. Two adjacent angles that form a straight line are a linear pair

pairlinear a are and 2pairlinear a are and 1 4.

CBADAB

5. Linear pairs are supplementary

21 6. 6. Supplements of congruent angles are congruent

arysupplement are and 2arysupplement are and 1 5.

CBADAB