Quadrilateral Proofs Page 4-5

(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

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

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

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

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

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

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

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

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

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

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