University:
Winston-Salem Forsyth County Schools
Course:
AP Calculus AB
Academic year:

2020
Views:

221

Pages:

2
Author:

IKolishi0ev0

Math III Unit 7-4 Theorems about Parallelograms Notes Name: ___________________________ 1. Prove opposite sides of parallelograms are congruent. G H Given: EFGH is a parallelogram Prove: EF ≅ HG ; FG ≅ EH E F Proof: 1. EFGH is a parallelogram Given 2. EF HG Definition of parallelogram 3. Draw transversal GE to form triangles Construction 4. ∠FGE ≅ ∠HEG and ∠FEG ≅ ∠HGE If 2 lines are cut by a trans., alt. int. ∠' s are ≅ 5. GE ≅ GE Reflexive 6. ∆EGH ≅ ∆GEF Angle-Side- Angle (ASA Congruence) 7. EF ≅ HG and FG ≅ EH CPCTC D C 2. Prove opposite angles of parallelograms are congruent. Given: ABCD is a parallelogram Prove: ∠A ≅ ∠C and ∠B ≅ ∠D A Proof: 1. ABCD is a parallelogram Given 2. AB DC Definition of parallelogram 3. Draw transversal AC to form triangles Construction 4. AB ≅ CD and AD ≅ CB Opposite sides of a parallelogram are ≅ 5. AC ≅ AC Reflexive 6. ∆ACD ≅ ∆CAB SSS Congruence 7. ∠B ≅ ∠D CPCTC 8. Draw transversal BD to form triangles Construction 9. AB ≅ CD and AD ≅ CB Opposite sides of a parallelogram are ≅ 10. BD ≅ BD Reflexive 11. ∆ABD ≅ ∆CDB SSS Congruence 12. ∠A ≅ ∠C CPCTC B T 3. Prove diagonals of parallelograms bisect each other. Given: QRST is a parallelogram with diagonals QS and TR . S M Prove: QS and TR bisect each other. Q Proof: 1. QRST is a parallelogram with diagonals QS and TR R Given 2. QR ≅ TS Opposite sides of a parallelogram are congruent. 3. ∠STR ≅ ∠QRT and ∠TSQ ≅ ∠RQS alternate interior angles are congruent 4. ∆QMR ≅ ∆SMT ASA Congruence. 5. QM ≅ SM and RM ≅ TM CPCTC 6. QS and TR bisect each other definition of bisector A B 4. Prove rectangles have congruent diagonals. Given: ABCD is a rectangle with diagonals AC and BD Prove: AC ≅ BD D Proof: 1. ABCD is a rectangle with diagonals AC and BD Given 2. AB ≅ DC and AD ≅ BC Opposite sides of a parallelogram are congruent. 3. ∠A , ∠B , ∠C , ∠D are right angles definition of rectangle 4. ∆BCD ≅ ∆ADC SAS Congruence 5. AC ≅ BD CPCTC C