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
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter9: Real Numbers And Right Triangles
Section9.3: The Pythagorean Theorem
Problem 31E
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 3 images
Recommended textbooks for you
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning