1. Quadrilateral Proofs
Page 4-5

2. (a) One pair of opposite side both parallel and congruent
Pg. 4 #1
(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

3. Statement Reason D C 1 2 A B 1. ABCD is a quadrilateral 1. Given
Pg. 4 #2
Statement
Reason
1. ABCD is a quadrilateral
1. Given D C 1
2. Given
3. Given
4. Two lines cut by a transversal that form congruent alternate interior angles are parallel 2 A B
5. ABCD is a parallelogram
5. A quadrilateral with one pair of opposite sides that are both parallel and congruent is a parallelogram

4. Statement Reason 1. PQRS is a quadrilateral 1. Given 2. Given 3. Given
Pg. 4 #3
Statement
Reason
1. PQRS is a quadrilateral
1. Given
2. Given
3. Given
4. Two lines cut by a transversal that form congruent alternate interior angles are parallel
5. PQRS is a parallelogram
5. A quadrilateral with both pairs of opposite sides parallel is a parallelogram

5. Statement Reason 1. Given 2. Given
Pg. 4 #5
Statement
Reason
1. Given
2. Given
3. A median extends from a vertex of a triangle to the midpoint of the opposite side
4. A midpoint divides a segment into 2 congruent parts
5. GJKL is a parallelogram
5. A quadrilateral with diagonals that bisect each other is a parallelogram

6. Statement Reason 1. Given 2. Given
Pg. 4 #8
Statement
Reason
1. Given
2. Given
3. Two adjacent angles that form a straight line are a linear pair
4. Linear pairs are supplementary
5. Supplements of the same angle are congruent
6. Two lines cut by a transversal that form congruent corresponding angles are parallel
7. Two lines cut by a transversal that form congruent alternate interior angles are parallel
8. ABCD is a parallelogram
8. A quadrilateral with both pairs of opposite sides parallel is a parallelogram

7. Statement Reason 1. PQRS is a parallelogram 1. Given 2. Given 3. Given
Pg. 4 #12
Statement
Reason
1. PQRS is a parallelogram
1. Given
2. Given
3. Given
4. Perpendicular segments form right angles
5. All right angles are congruent
6. Opposite sides of a parallelogram are both parallel and congruent
7. Parallel lines cut by a transversal form congruent alternate interior angles
9. CPCTC

8. Statement Reason 1. ABCD is a rectangle 1. Given 2. Given
Pg. 5 #1
Statement
Reason
1. ABCD is a rectangle
1. Given
2. Given
3. All angles of a rectangle are congruent
4. Opposite sides of a rectangle are congruent
5. A midpoint divides a segment into two congruent parts
7. CPCTC

9. Statement Reason 1. ABCD is a rectangle 1. Given
Pg. 5 #2
Statement
Reason
1. ABCD is a rectangle
1. Given
2. Opposite sides of a rectangle are congruent
3. Reflexive postulate
4. All angles of a rectangle are congruent
6. CPCTC
7. A triangle with two congruent base angles is isosceles

10. Statement Reason 1. ABCD is a rhombus 1. Given 2. Given
Pg. 5 #3
Statement
Reason
1. ABCD is a rhombus
1. Given
2. Given
3. All sides of a rhombus are congruent
4. Reflexive postulate
6. CPCTC

11. Statement Reason 1. AECB is a rhombus 1. Given 2. Given
Pg. 5 #4
Statement
Reason
1. AECB is a rhombus
1. Given
2. Given
3. All sides of a rhombus are congruent
4. Vertical angles are congruent
5. Opposite angles of a rhombus are congruent
6. Subtraction postulate
7. Partition postulate
8. Substitution postulate
10. CPCTC

12. Statement Reason 1. ABCD is an isosceles trapezoid 1. Given 2. Given
Pg. 5 #8
Statement
Reason
1. ABCD is an isosceles trapezoid
1. Given
2. Given
3. Base angles of an isosceles trapezoid are congruent
4. Two adjacent angles that form a straight line are a linear pair
5. Linear pairs are supplementary
6. Supplements of congruent angles are congruent