http://www.ck12.org Chapter 6. Polygons and Quadrilaterals
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CK-12 Foundation: Chapter6ParallelogramClassificationB
Concept Problem Revisited
In order for the patio to be a rectangle, first the opposite sides must be congruent. So, two sides are 21ft and two are
28 ft. To ensure that the parallelogram is a rectangle without
d^2 = 212 + 282 = 441 + 784 = 1225
d=
√
1225 = 35 f t
Vocabulary
Aparallelogramis a quadrilateral with two pairs of parallel sides.
A quadrilateral is arectangleif and only if it has four right (congruent) angles:
A quadrilateral is arhombusif and only if it has four congruent sides:
A quadrilateral is asquareif and only if it has four right angles and four congruent sides.
Guided Practice
- Is a rectangle SOMETIMES, ALWAYS, or NEVER a parallelogram? Explain why.
- Is a rhombus SOMETIMES, ALWAYS, or NEVER equiangular? Explain why.
- Is a quadrilateral SOMETIMES, ALWAYS, or NEVER a pentagon? Explain why.
Answers:
- A rectangle has two sets of parallel sides, so it is ALWAYS a parallelogram.
- Any quadrilateral, including a rhombus, is only equiangular if all its angles are 90◦. This means a rhombus is
SOMETIMES equiangular, only when it is a square. - A quadrilateral has four sides, so it will NEVER be a pentagon with five sides.
Practice
1.RACEis a rectangle. Find:
a.RG
b.AE
c.AC
d.EC
e.m^6 RAC
2.DIAMis a rhombus. Find:
a.MA