Ch 8.4

A rhombus is a parallelogram that has four congruent sides.

That means that the opposite sides must also be parallel.

The diagonals of a rhombus form perpendicular lines.

The diagonals bisect the interior angles.

A rectangle is a parallelogram with 4 right angles.

Therefore, opposite sides must also be parallel.

The diagonals of a rectangle are congruent.

A square is a parallelogram with 4 right angles AND 4 congruent sides.

Because a parallelogram has parallel opposite sides, a square has parallel opposite sides.

A trapezoid is a quadrilateral with 1 pair of parallel sides.

Can any square be a rectangle? Yes!

Can any rectangle be a square? No!

Can any square be a rhombus? Yes!

Can any rectangle be a rhombus? No!

m<A = m<C

ALWAYALWAYSS

m<B = m<C

SometimeSometimess

m<B = m<D

ALWAYALWAYSSAB = BC ALWAYALWAYSSAB = DC ALWAYALWAY

SS

M<A = m<C

ALWAYALWAYSS

m<B = m<C

ALWAYSALWAYS

m<B = m<D

ALWAYALWAYSSAB = BC SometimeSometime

ssAB = DC ALWAYALWAYSS

Rhombus 5x + 6 = 8x6 = 3x2 = x

< Q and < P should be supplementary!12y – 1 + 97 = 180 12y + 96 = 180 12y = 84

y = 7

Square 2x + 1 = 4x - 72x + 8 = 4x8 = 2x

< KLN and < NLM should be complementary!7y + 3 + 45 = 90

7y + 48 = 90 7y = 42

y = 6

4 = x

YZ

The diagonals bisect the interior angles.

A rhombus is a parallelogram that has four congruent sides.

That means that the opposite sides must also be parallel.

The diagonals of a rhombus form perpendicular lines.

34º34º

34º34º34º34º56º56º56º56º

56º56º56º56º

12.512.5

12.512.5

12.512.512.512.510.410.4

SOH CAH TOA!

Cos(56) = 7/x7/Cos(56) = x12.5 = x

m<TPQ

m<PST

m<PTQ

PS

PRHINT: PTQ is what kind of triangle?

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Practice, Practice, Practice Chapter 8-4