properties of parallelograms
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
Properties of Parallelograms
Parallelogram• A quadrilateral with both pairs of opposite sides parallel
Properties
Opposite sides are congruent
Opposite angles are congruent
Consecutive angles are supplementary.
ADD UP TO 180°
Diagonals bisect each other.
This cuts the diagonals into two equal parts.
• A diagonal makes 2 congruent triangles
ABCD is a parallelogram. Find the lengths and the angle measures.
1. AD
2. EC
3. mADC
4. mBCD
B 8 C
A D
6545
E
5
85
110
70
Find the value of each variable in the parallelogram.
4y
x = 5
2y42x – 6
y = 30
Proofs Involving Parallelograms A E B 2
1D C
3G F
Given: ABCD and AEFG are parallelograms
Prove: <1 = < 3
Statements Reasons
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Plan: Show that both angles are congruent to <2
1. ABCD & AEFG are Parallelograms 1. Given2. <1 = < 2 2. Opposite Angles3. <2 = <3 3. Opposite Angles 4. <1 = <3 4. Transitive ~
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Proving Theorem 6.2
Given: ABCD is a parallelogram
Prove: AB = CD, AD = CB
Statements Reasons
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A B
D C
Plan: Insert a diagonal which will allow us to divide the parallelogram into two triangles
1. ABCD is a parallelogram 1. Given2. AB || CD, and AD || CB 2. Def. of a parallelogram
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3. <ABD = < CDB 3. Alternate Int4. <ADB = < CBD 4. Alternate Int6. DB = DB 6. Reflexive7. /\ ADB = /\ CBD 7. ASA8. AB = CD, AD = CB 8. CPCTC
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Given: /\ RQP = /\ ONP R is the midpoint of MQProve: MRON is a parallelogram
Statements Reasons
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Q
R P O
M N
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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