Post on 17-Dec-2015
transcript
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