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Published byLora Horton Modified over 6 years ago
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Date: Topic: Rhombi, Rectangles, and Squares (7.2)
Warm-up: A B 2x + 5 Find x. 2x + 5 2x x + 5 = 50 4x + 10 = 50 C D -10 -10 4x = 40 4 4 x = 10
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Rhombus 10 cm A rhombus is a quadrilateral with two sets of parallel sides and all four congruent sides. 10 cm 10 cm 10 cm Since a rhombus is a special parallelogram, it has all the properties of a parallelogram : - Opposite angles are congruent. - Opposite sides are congruent. - The diagonals bisect each other.
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Properties of a Rhombus
A Rhombus also has its own unique properties: The diagonals bisect the angles. The diagonals are perpendicular bisectors of each other. Because of this, the diagonals of a rhombus create four congruent right triangles.
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Rectangle A rectangle is a parallelogram with four 90 degree angles.
20 cm 5 cm 5 cm 20 cm Since a rectangle is a special parallelogram, it has all the properties of a parallelogram : - Opposite angles are congruent. - Opposite sides are congruent. - The diagonals bisect each other.
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Properties of a Rectangle
B D C Rectangles also have their own unique properties: - The diagonals of a rectangle are congruent. - The diagonal bisections are congruent.
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Square A B A square is a rhombus (4 congruent sides and 2 sets of parallel sides) with four 90 degree angles (like a rectangle). A square is a special type of rectangle, so it also has congruent diagonals. D C Since a square is also a special kind of rhombus, it has all the properties of a rhombus and some of unique ones: - Diagonals bisect the angles (all are congruent). - Diagonals are perpendicular bisectors of each other (all bisected segments are congruent). - Diagonals form four congruent isosceles right triangles.
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The diagonals of a rhombus are perpendicular bisectors of each other.
Find the missing angle measurements. This shape is a rhombus. 5 4 90° 1 The diagonals of a rhombus are perpendicular bisectors of each other. 2 90° 3 35° 35° The diagonals of a rhombus are angle bisectors.
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-125° -125° The angles of a triangle add up to 180 degrees. 5 4 55°
90° 55° -125° -125° 90° 35° 35° The diagonals of a rhombus are angle bisectors.
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