Quadrilateral Proofs Page 6. Pg. 6 #1 StatementReason 2. Given 3. Given Pg. 6 #3 6. Opposite sides of a parallelogram are both parallel and congruent.

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Presentation transcript:

Quadrilateral Proofs Page 6

Pg. 6 #1

StatementReason 2. Given 3. Given Pg. 6 #3 6. Opposite sides of a parallelogram are both parallel and congruent 1. Given1. FLSH is a parallelogram 4. Perpendicular segments form right angles 5. All right angles are congruent 7. Parallel lines cut by a transversal form congruent alternate interior angles F L S H A G

StatementReason Pg. 7 #7 2. Opposite sides of a parallelogram are parallel 1. Given1. ABCD is a parallelogram 3. Parallel lines cut by a transversal form congruent alternate interior angles 4. An exterior angle of a triangle is greater than either of its non-adjacent interior angles 5. Substitution postulate of inequalities D A B C 1 2

StatementReason Pg Given 1. Given1. DCTV is a parallelogram 3. Parallel lines cut by a transversal form congruent alternate interior angles 4. Opposite sides of a parallelogram are both parallel and congruent 5. Parallel lines cut by a transversal form congruent alternate interior angles 7. CPCTC D V T C S B

StatementReason Pg. 2. Given 1. Given1. ABCD is a parallelogram 3. A segment bisector divides a segment into 2 congruent parts 4. Opposite sides of a parallelogram are parallel 5. Parallel lines cut by a transversal form congruent alternate interior angles 8. CPCTC A D C B G F E 6. Vertical angles are congruent 4

StatementReason Pg. 2. Given 1. Given1. ABCD is a parallelogram 7. Parallel lines cut by a transversal form congruent alternate interior angles A D C B F 3. Given 4. Perpendicular segments form right angles 5. All right angles are congruent 9. CPCTC 6. Opposite sides of a parallelogram are both congruent and parallel. E

StatementReason Pg. 2. Given 1. Given1. ABCD is a parallelogram 4. Parallel lines cut by a transversal form congruent alternate interior angles A D C B 1 2 E 3. Opposite sides of a parallelogram are both congruent and parallel. F

StatementReason Pg. 2. Given 1. Given1. ABCD is a quadrilateral 7. CPCTC A D C B F 3. Given 4. Perpendicular segments form right angles 5. All right angles are congruent 8. CPCTC 9. 2 lines cut by a transversal that form congruent alternate interior angles are parallel 10. A quadrilateral with one pair of opposite sides both congruent and parallel is a parallelogram 10. ABCD is a parallelogram E

StatementReason Pg. 2. Given 1. Given1. D is the midpoint of 3. A midpoint divides a segment into 2 congruent parts 5. Vertical angles are congruent 9. CPCTC A D C B 3 4 E F 7. CPCTC A segment bisector divides a segment into 2 congruent parts 8. 2 lines cut by a transversal that form congruent alternate interior angles are parallel 10. Substitution postulate 11. A quadrilateral with one pair of opposite sides both congruent and parallel is a parallelogram 11. ACFD is a parallelogram

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