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.

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Presentation transcript:

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A rectangle is a parallelogram with 4 right angles. TTherefore, opposite sides must also be parallel. T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<CALWAYS m <B = m<CSometimes m <B = m<DALWAYS AB = BCALWAYS AB = DCALWAYS

M <A = m<CALWAYS m <B = m<CALWAYS m <B = m<DALWAYS AB = BC Sometimes AB = DCALWAYS

Rhombus 5x + 6 = 8x 6 = 3x 2 = x < Q and < P should be supplementary! 12y – = y + 96 = y = 84 y = 7

Square 2x + 1 = 4x - 7 2x + 8 = 4x 8 = 2x < KLN and < NLM should be complementary! 7y = 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. 34º 34º 34º 56º 56º 56º 56º SOH CAH TOA! Cos(56) = 7/x 7/Cos(56) = x 12.5 = x

m <TPQ m <PST m <PTQ PS PR HINT: PTQ is what kind of triangle?

  Practice, Practice, Practice  Chapter 8-4