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Properties of Parallelograms

Properties of Parallelograms. Parallelogram. A quadrilateral with both pairs of opposite sides parallel. Properties. Opposite sides are congruent. Opposite angles are congruent. ADD UP TO 180°. Consecutive angles are supplementary. Diagonals bisect each other.

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Properties of Parallelograms

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  1. Properties of Parallelograms

  2. Parallelogram • A quadrilateral with both pairs of opposite sides parallel

  3. Properties

  4. Opposite sides are congruent

  5. Opposite angles are congruent

  6. ADD UP TO 180° Consecutive angles are supplementary.

  7. Diagonals bisect each other. This cuts the diagonals into two equal parts.

  8. A diagonal makes 2 congruent triangles

  9. B 8 C A D 45 65 E 5 ABCD is a parallelogram. Find the lengths and the angle measures. 8 5 • AD • EC • mADC • mBCD 110 70

  10. Find the value of each variable in the parallelogram. x = 5 2x – 6 4 y = 30 2y 4y

  11. A E B 2 1 D C 3 G F Given: ABCD and AEFG are parallelograms Prove: <1 = < 3 Statements Reasons ~ • ABCD & AEFG are Parallelograms 1. Given • <1 = < 2 2. Opposite Angles • <2 = <3 3. Opposite Angles • <1 = <3 4. Transitive ~ ~ ~ Proofs Involving Parallelograms Plan: Show that both angles are congruent to <2

  12. A B D C Given: ABCD is a parallelogram Prove: AB = CD, AD = CB Statements Reasons _ _ _ _ ~ ~ • ABCD is a parallelogram 1. Given • 2. AB || CD, and AD || CB 2. Def. of a parallelogram __ __ __ __ ~ 3. <ABD = < CDB 3. Alternate Int 4. <ADB = < CBD 4. Alternate Int 6. DB = DB 6. Reflexive 7. /\ ADB = /\ CBD 7. ASA 8. AB = CD, AD = CB 8. CPCTC ~ __ __ ~ ~ __ __ __ __ ~ ~ Proving Theorem 6.2 Plan: Insert a diagonal which will allow us to divide the parallelogram into two triangles

  13. Q R P O M N ~ Given: /\ RQP = /\ ONP R is the midpoint of MQ Prove: MRON is a parallelogram Statements Reasons __ ~ 1. /\ RQP = /\ ONP 1. Given R is the midpoint of MQ 2. MR = RQ 2. Definition of a midpoint 3. RQ = NO 3. CPCTC 4. MR = NO 4. Transitive 5. <QRP = < NOP 5. CPCTC 6. MQ || NO 6. Alternate Interior 7. MRON is a parallelogram 7. Definition __ __ ~ __ __ ~ __ __ ~ ~ __ __

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