Properties of Rhombuses, Rectangles, and Squares

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Presentation transcript:

Properties of Rhombuses, Rectangles, and Squares

What is a rhombus? 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.

Rhombus cont… The diagonals bisect the interior angles.

Rectangles A rectangle is a parallelogram with 4 right angles. Therefore, opposite sides must also be parallel. The diagonals of a rectangle are congruent.

Squares 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.

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

Can it be…? Can any square be a rectangle? Yes! Can any rectangle be a square? No! Can any square be a rhombus? Can any rectangle be a rhombus?

m<A = m<C ALWAYS m<B = m<C Sometimes m<B = m<D Suppose you have a rhombus ABCD… When are the following true? Sometimes, never, or always A B C D m<A = m<C ALWAYS m<B = m<C Sometimes m<B = m<D ALWAYS AB = BC ALWAYS AB = DC ALWAYS

M<A = m<C ALWAYS m<B = m<C ALWAYS m<B = m<D ALWAYS Suppose you have a rectangle ABCD… when are the following true? Always? Never? Sometimes? A B C D M<A = m<C ALWAYS m<B = m<C ALWAYS m<B = m<D ALWAYS Sometimes AB = BC AB = DC ALWAYS

One of these is not a rhombus… which one is not a rhombus?

First classify the quadrilateral then find x and y Rhombus 5x + 6 = 8x 6 = 3x 2 = x < Q and < P should be supplementary! 12y – 1 + 97 = 180 12y + 96 = 180 12y = 84 y = 7

First classify the quadrilateral then find x and y Square 2x + 1 = 4x - 7 2x + 8 = 4x 8 = 2x 4 = x < KLN and < NLM should be complementary! 7y + 3 + 45 = 90 7y + 48 = 90 7y = 42 y = 6

Given that WXYZ is a rhombus…what do we know about the figure? 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. 12.5 34º 56º 56º 34º 12.5 12.5 10.4 34º 56º 56º Z Y 12.5 Cos(56) = 7/x 7/Cos(56) = x 12.5 = x SOH CAH TOA!

The figure below is a rectangle Find the missing angles and sides m<TPQ m<PST m<PTQ PS PR HINT: PTQ is what kind of triangle?