6-4: squares and rhombi expectations: g1.4.1: solve multistep problems and construct proofs...
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6-4: Squares and Rhombi
Expectations:G1.4.1: Solve multistep problems and construct
proofs involving angle measure, side length, diagonal length, perimeter, and area of squares, rectangles, parallelograms, kites, and trapezoids.
G1.4.2: Solve multistep problems and construct proofs involving quadrilaterals (e.g., prove that the diagonals of a rhombus are perpendicular) using Euclidean methods or coordinate geometry.
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Rhombus
Defn: Rhombus: A quadrilateral is a rhombus iff all 4 sides are congruent. The plural or rhombus is rhombi.
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Properties of a Rhombus Theorem
If a quadrilateral is a rhombus, then:
a.it is a parallelogram.
b. the diagonals are perpendicular to each other.
c. each diagonal bisects a pair of opposite angles.
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Prove a rhombus is a parallelogram.
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The figure below is a rhombus. Solve for x.
10x - 24
6x+12
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Sufficient Condition for a Rhombus Theorem
If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.
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Determine the value of x so that the parallelogram is a rhombus.
(15x – 30)
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Square
Defn: Square: A parallelogram is a square iff it is a rectangle and a rhombus.
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What is true about the diagonals of a square?
a.congruent (rectangle),
b. perpendicular (rhombus),
c. bisect a pair of opposite angles (rhombus),
d. bisect each other (parallelogram)
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WXYZ is a quadrilateral. Of the terms parallelogram, rectangle, rhombus, square which apply to WXYZ?
W(5,5), X(10,5), Y(10,10), Z(5,10)
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Which of the following is a property of squares, but not rhombi?
A) Diagonals are perpendicularB) Diagonals are congruentC) Consecutive sides are congruentD) Consecutive angles are supplementaryE) Opposite angles are congruent
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Prove the diagonals of a square are congruent.
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Assignment
Pages 317 – 318,# 21 – 35, 39 – 47 (odds)
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