1. TEQ – Typical Exam Questions

2. J Q P M K L O Given: JKLM is a parallelogram Prove: StatementReason 2. Given 1. Given1. JKLM is a parallelogram 3. Opposite sides of a parallelogram are parallel 4. Parallel lines cut by a transversal form congruent alternate interior angles 5. Vertical angles are congruent 1 2 3 4 7. CPCTC TEQ #1

3. Given: Parallelogram DEBK,, Prove: C J L D B K E A StatementReason 1. Parallelogram DEBK 2. 1. Given 2. Given 3. Given 5. Addition postulate 6. Partition postulate 7. Substitution postulate 4. Reflexive postulate 8. Opposite sides of a parallelogram are parallel 9. Parallel lines cut by a transversal form congruent alternate interior angles. 11. CPCTC

4. StatementReason 2. Given 3. Given TEQ #3 6. Opposite sides of a parallelogram are both parallel and congruent 1. Given1. ABCD 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 A D C B 1 2 4 3 E F Given: Parallelogram ABCD, Prove:

5. StatementReason S PQ 1. Given TEQ #4 R 2. Given 2 1 3. Assumption 4. PQRS is a rhombus 4. A parallelogram whose diagonal bisects an angle is a rhombus 5. All sides of a rhombus are congruent 6. Contradiction 2,5

6. StatementReason TEQ #5 2. Given 1. Given1. Rhombus ABCD 3. A midpoint divides a segment into two congruent parts 4. Vertical angles are congruent 8. CPCTC 6. Parallel lines cut by a transversal form congruent alternate interior angles. 5. Opposite sides of a rhombus are parallel 9. All sides of a rhombus are congruent 10. Substitution postulate 1 2 3 4

7. StatementReason TEQ #6 2. Given 1. Given1. ABDE is a parallelogram 3. Opposite sides of a parallelogram are congruent 4. Substitution postulate 5. A triangle with two congruent sides is isosceles Given: ABDE is a parallelogram

8. StatementReason TEQ #7 2. Given 1. Given 3. A segment bisector divides a segment into two congruent parts 7. Two lines cut by a transversal that form congruent alternate interior angles are parallel 6. CPCTC A D C B 2 1 3 E 4. Vertical angles are congruent 4 8. A quadrilateral that has one pair of opposite sides both parallel and congruent is a parallelogram

9. StatementReason TEQ #9 2. Given 1. Given 3. Assumption 4. Reflexive postulate 6. CPCTC 7. Contradiction 2,6

10. StatementReason TEQ #10 3. Opposite sides of a parallelogram are congruent 1. Given1. ABCD is a parallelogram 4. Opposite angles of a parallelogram are congruent Prove: D E F A C B Given: ABCD is a parallelogram 2. Given

11. StatementReason 2. Given 1. Given1. ABCD is a parallelogram 7. Parallel lines cut by a transversal form congruent alternate interior angles A D C B 1 2 4 3 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

12. StatementReason S P Q 1. Given TEQ #8 R 2. Given 3. Assumption 4. A midpoint divides a segment into two congruent parts. 5. Vertical angles are congruent T 7. CPCTC 8. Contradiction 1,7