Report

TEQ – Typical Exam Questions TEQ #1 Statement J P K 1 3 O 4 M 2 1. JKLM is a parallelogram 1. Given 2. JO OL 2. Given 3. JPK MQL 3. Opposite sides of a parallelogram are parallel 4. 1 2 4. Parallel lines cut by a transversal form congruent alternate interior angles 5. 3 4 5. Vertical angles are congruent 6. ΔJOP ΔLOQ 6. ASA ASA 7. OP OQ 7. CPCTC L Q Given: JKLM is a parallelogram JO OL Prove: OP OQ Reason E C B Statement L J D A K Given: Parallelogram DEBK, , BC DA DJ BL Prove: CJ AL Reason 1. Parallelogram DEBK 1. Given 2. BC DA 2. Given 3. DJ BL 3. Given 4. JL JL 4. Reflexive postulate 5. DJ JL BL JL 5. Addition postulate 6. DJ JL DL 6. Partition postulate BL JL JB 7. DL JB 7. Substitution postulate 8. EB DK 8. Opposite sides of a parallelogram are parallel 9. 1 2 9. Parallel lines cut by a transversal form congruent alternate interior angles. 10. ΔCJB ΔALD 10. SAS SAS 11. CJ AL 11. CPCTC TEQ #3 Statement D 4 1 F A E 2 3 B 1. ABCD is a parallelogram 1. Given 2. DF AC 2. Given C 3. EB AC 4. 1 and 2 are right angles Prove: DF BE 3. Given 4. Perpendicular segments form right angles 5. 1 2 5. All right angles are congruent 6. DC AB and DC AB 6. Opposite sides of a parallelogram are both parallel and congruent 7. 3 4 7. Parallel lines cut by a transversal form congruent alternate interior angles 8. ΔDFC ΔBEA 8. AAS AAS 9. DF BE 9. CPCTC Given: Parallelogram ABCD, DF AC Reason TEQ #4 Statement S R 1 P 2 Q Given : Parallelogram PQRS PQ QR Prove: 1 is not congruent to2 Reason 1. Parallelogram PQRS 1. Given 2. PQ QR 2. Given 3. ∠1 ≅ ∠2 3. Assumption 4. PQRS is a rhombus 4. A parallelogram whose diagonal bisects an angle is a rhombus 5. ≅ 5. All sides of a rhombus are congruent 6. ∠1 ∠2 6. Contradiction 2,5 TEQ #5 Statement 1. Rhombus ABCD Reason 1. Given 2. E is the midpoint of 2. Given 4 1 3. DE EF 3. A midpoint divides a segment into two congruent parts 4. 1 2 4. Vertical angles are congruent 5. DC ABF 5. Opposite sides of a rhombus are parallel 6. 3 4 6. Parallel lines cut by a transversal form congruent alternate interior angles. 7. ΔDEC ΔFEB 7. ASA ASA 8. DC BF 8. CPCTC 9. DC DA 9. All sides of a rhombus are congruent 10. AD BF 10. Substitution postulate 2 3 TEQ #6 Statement Reason 1. ABDE is a parallelogram 1. Given 2. AE DC 2. Given 3. AE BD 3. Opposite sides of a parallelogram are congruent 4. DC BD 4. Substitution postulate 5. DBC is isosceles 5. A triangle with two congruent sides is isosceles Given: ABDE is a parallelogram AE DC Prove : DBC is isosceles TEQ #7 Statement D C E 4 2 3 1 A B Reason 1. DB bisects AC 1. Given 2. 1 2 2. Given 3. AE EC 3. A segment bisector divides a segment into two congruent parts 4. 3 4 4. Vertical angles are congruent 5. ΔAED ΔCEB 5. ASA ASA 6. DA BC 6. CPCTC 7. AD BC 7. Two lines cut by a transversal that form congruent alternate interior angles are parallel 8. ABCD is a parallelogram 8. A quadrilateral that has one pair of opposite sides both parallel and congruent is a parallelogram TEQ #9 Statement Reason 1. AB BC 1. Given 2. BD BE 2. Given 3. A C 3. Assumption 4 . B B 4. Reflexive postulate 5. ABE CBD 5. ASA ASA 6. BD BE 7. A C 6. CPCTC 7. Contradiction 2,6 TEQ #10 Statement D A E F C B 1. ABCD is a parallelogram 1. Given 2. AE FC 3. DA CB 2. Given Prove: ΔDAE ΔBCF 3. Opposite sides of a parallelogram are congruent 4. A C 4. Opposite angles of a parallelogram are congruent 5. ΔDAE ΔBCF 5. SAS SAS Given: ABCD is a parallelogram AE FC Reason Statement D F 4 A 1 C 2 E B 3 Reason 1. ABCD is a parallelogram 1. Given 2. DE AC 3. BF AC 2. Given 3. Given 4. 1 and 2 are right angles 4. Perpendicular segments form right angles 5. 1 2 5. All right angles are congruent 6. DA CB , DA CB 6. Opposite sides of a parallelogram are both congruent and parallel. 7. 3 4 7. Parallel lines cut by a transversal form congruent alternate interior angles 8. ΔDEA ΔBFC 8. AAS AAS 9. AE FC 9. CPCTC Prove: AE FC TEQ #8 Q P Statement T R Reason 1. PQ RS 1. Given 2. PQ and RS intersect at T 2. Given 3. T is the midpoint of PS and RQ 3. Assumption 4. ≅ , ≅ 4. A midpoint divides a segment into two congruent parts. 5. ∠1 ≅ ∠2 5. Vertical angles are congruent 6. ∆ ≅ ∆ 6. ≅ S Given : PQ RS 7. ≅ PQ and RS intersect at T 8.T is not the midpoint of PS and RQ Prove : T is not the midpoint of PS and RQ 7. CPCTC 8. Contradiction 1,7