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PROPERTIES OF PARALLELOGRAM ABCD is a parallelogram. 1. In a parallelogram, any two opposite sides are congruent. AD and BC are opposite sides, AB and CD are also opposite sides. Therefore, they are congruent (E). AD = BC and AB = CD Ex. If AD = 10, then BC 10. 2. In a parallelogram, any two opposite angles are congruent. LADC and 2CBA are opposite angles, LDAB and LBCD are also opposite sides. Therefore, they are congruent (=). LADC = LCBA and LDAB = ZBCD Ex. If LADC = 70°, then LCBA = 70°. %3D 3. In a parallelogram, any two consecutive angles are supplementary. LA and ZB are consecutive angles, therefore they are supplementary (= 180). LC + ZD = 180 LA + LD = 180 Ex. If ZA = 100°, then what is the mzB? LA + LB = 180 %3D %3D ZB + LC = 180 %3D %3D LA + LB = 180° %3D 100° + ZB = 180° ZB = 180° - 100° ZB = 80° %3D 4. The diagonals of a parallelogram bisect each other. AC and BD are diagonals and they bisect each other at E. AE = EC Ex. If AE = 3x – 11 and EC = x + 3, then what is x? DE = EB %3D AE = EC 3x – 11 = x + 3 3x - x = 3 + 11 2x = 14 x = 7 5. A diagonal of a parallelogram forms two congruent triangles. ABAD = ADCB AADC = ACBA

PROPERTIES OF PARALLELOGRAM ABCD is a parallelogram. 1. In a parallelogram, any two opposite sides are congruent. AD and BC are opposite sides, AB and CD are also opposite sides. Therefore, they are congruent (E). AD = BC and AB = CD Ex. If AD = 10, then BC 10. 2. In a parallelogram, any two opposite angles are congruent. LADC and 2CBA are opposite angles, LDAB and LBCD are also opposite sides. Therefore, they are congruent (=). LADC = LCBA and LDAB = ZBCD Ex. If LADC = 70°, then LCBA = 70°. %3D 3. In a parallelogram, any two consecutive angles are supplementary. LA and ZB are consecutive angles, therefore they are supplementary (= 180). LC + ZD = 180 LA + LD = 180 Ex. If ZA = 100°, then what is the mzB? LA + LB = 180 %3D %3D ZB + LC = 180 %3D %3D LA + LB = 180° %3D 100° + ZB = 180° ZB = 180° - 100° ZB = 80° %3D 4. The diagonals of a parallelogram bisect each other. AC and BD are diagonals and they bisect each other at E. AE = EC Ex. If AE = 3x – 11 and EC = x + 3, then what is x? DE = EB %3D AE = EC 3x – 11 = x + 3 3x - x = 3 + 11 2x = 14 x = 7 5. A diagonal of a parallelogram forms two congruent triangles. ABAD = ADCB AADC = ACBA

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter10: Measurement, Area, And Volume
Section10.2: Polygons And Quadrilaterals
Problem 23E
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PROPERTIES OF PARALLELOGRAM ABCD is a parallelogram. 1. In a parallelogram, any two opposite sides are congruent. AD and BC are opposite sides, AB and CD are also opposite sides. Therefore, they are congruent (=). AD = BC and AB = CD Ex. If AD = 10, then BC 10. %3D 2. In a parallelogram, any two opposite angles are congruent. LADC and 2CBA are opposite angles, LDAB and LBCD are also opposite sides. Therefore, they are congruent (). LADC = LCBA and LDAB = <BCD Ex. If LADC = 70°, then LCBA = 70°. %3D 3. In a parallelogram, any two consecutive angles are supplementary. LA and ZB are consecutive angles, therefore they are supplementary (= 180). LA + LB = 180 LC + ZD = 180 LA + LD = 180 Ex. If ZA = 100°, then what is the mzB? %3D ZB + LC = 180 %3D %3D LA + LB = 180° %3D 100° + ZB = 180° ZB = 180° - 100° %3D ZB = 80° 4. The diagonals of a parallelogram bisect each other. AC and BD are diagonals and they bisect each other at E. AE = EC Ex. If AE = 3x - 11 and EC = x + 3, then what is x? DE = EB %3D AE = EC 3x – 11 = x + 3 3x - x = 3 + 11 2x = 14 x = 7 5. A diagonal of a parallelogram forms two congruent triangles. ABAD = ADCB AADC = ACBA
Transcribed Image Text:PROPERTIES OF PARALLELOGRAM ABCD is a parallelogram. 1. In a parallelogram, any two opposite sides are congruent. AD and BC are opposite sides, AB and CD are also opposite sides. Therefore, they are congruent (=). AD = BC and AB = CD Ex. If AD = 10, then BC 10. %3D 2. In a parallelogram, any two opposite angles are congruent. LADC and 2CBA are opposite angles, LDAB and LBCD are also opposite sides. Therefore, they are congruent (). LADC = LCBA and LDAB = <BCD Ex. If LADC = 70°, then LCBA = 70°. %3D 3. In a parallelogram, any two consecutive angles are supplementary. LA and ZB are consecutive angles, therefore they are supplementary (= 180). LA + LB = 180 LC + ZD = 180 LA + LD = 180 Ex. If ZA = 100°, then what is the mzB? %3D ZB + LC = 180 %3D %3D LA + LB = 180° %3D 100° + ZB = 180° ZB = 180° - 100° %3D ZB = 80° 4. The diagonals of a parallelogram bisect each other. AC and BD are diagonals and they bisect each other at E. AE = EC Ex. If AE = 3x - 11 and EC = x + 3, then what is x? DE = EB %3D AE = EC 3x – 11 = x + 3 3x - x = 3 + 11 2x = 14 x = 7 5. A diagonal of a parallelogram forms two congruent triangles. ABAD = ADCB AADC = ACBA
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