CK-12 Geometry Concepts

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

1. Is a rectangle SOMETIMES, ALWAYS, or NEVER a parallelogram? Explain why.


2. Is a rhombus SOMETIMES, ALWAYS, or NEVER equiangular? Explain why.


3. Is a quadrilateral SOMETIMES, ALWAYS, or NEVER a pentagon? Explain why.

Answers:

1. A rectangle has two sets of parallel sides, so it is ALWAYS a parallelogram.


2. 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.


3. 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