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MG2.3 Draw quadrilaterals and triangles from given information about them (e.g., a quadrilateral having equal sides but no right angles, a right isosceles triangle.) California Standards

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Vocabulary parallelogram rectangle rhombus square trapezoid

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**Some quadrilaterals have properties that classify them as special quadrilaterals.**

Parallelogram Both pairs of opposite sides are parallel. You can also classify a quadrilateral as a parallelogram if both pairs of opposite sides or both pairs of opposite angles are congruent.

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**A rectangle is a parallelogram with four right angles.**

A rhombus is a parallelogram with four congruent sides.

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**A square is a parallelogram with four congruent sides and four right angles.**

A trapezoid has exactly one pair of opposite sides that are parallel.

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**Quadrilaterals can have more than one**

name because the special quadrilaterals sometimes share properties.

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**Additional Example 1: Classifying Quadrilaterals**

Give all the names that apply to the quadrilateral. Then give the name that best describes it. A. This figure has two pairs of parallel sides, so it is a parallelogram. It has four congruent sides, so it is also a rhombus. Rhombus best describes this quadrilateral.

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**Additional Example 1: Identifying Types of Quadrilaterals**

Give all the names that apply to the quadrilateral. Then give the name that best describes it. B. The figure has exactly one pair of opposite sides that is parallel, so it is a trapezoid. Trapezoid best describes this quadrilateral.

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**Additional Example 1: Identifying Types of Quadrilaterals**

Give all the names that apply to the quadrilateral. Then give the name that best describes it. C. The figure has two pairs of parallel sides, so it is a parallelogram. It has four right angles, so it is also a rectangle. Rectangle best describes this quadrilateral.

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**Additional Example 1: Identifying Types of Quadrilaterals**

Give all the names that apply to the quadrilateral. Then give the name that best describes it. D. The figure has two pairs of parallel sides and both pairs of opposite angles are congruent, so it is a parallelogram. Parallelogram best describes this quadrilateral.

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**It has four right angles, so it is also a rectangle.**

Check It Out! Example 1 Give all the names that apply to the quadrilateral. Then give the name that best describes it. A. This figure has two pairs of parallel sides, so it is called a parallelogram. It has four right angles, so it is also a rectangle. Rectangle best describes this quadrilateral.

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**The figure has two pairs of parallel sides, so it is a parallelogram.**

Check It Out! Example 1 Give all the names that apply to the quadrilateral. Then give the name that best describes it. B. The figure has two pairs of parallel sides, so it is a parallelogram. It has four congruent sides, so it is also a rhombus. It does not have four right angles, so it is not a square or rectangle. Rhombus best describes this quadrilateral.

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**Square best describes this quadrilateral.**

Check It Out! Example 1 Give all the names that apply to the quadrilateral. Then give the name that best describes it. C. The figure has two pairs of opposite sides that are parallel, so it is a parallelogram. It has four right angles, so it is also a rectangle. It has four congruent sides, so it is also a rhombus and a square. Square best describes this quadrilateral.

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**Additional Example 2: Drawing Quadrilaterals**

Draw each figure. If it is not possible to draw explain why. A. a rectangle that is not a rhombus. The figure has opposite sides that are parallel but does not have four congruent sides.

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**Additional Example 2: Drawing Quadrilaterals**

Draw each figure. If it is not possible to draw explain why. B. a square that is not a rhombus. Not possible; all squares are rhombi because they have 4 congruent sides.

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Check It Out! Example 2 Draw each figure. If it is not possible to draw explain why. A. a trapezoid that is a rectangle. Not possible; A rectangle has four right angles and a trapezoid does not.

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**Draw each figure. If it is not possible to draw explain why.**

Check It Out! Example 2 Draw each figure. If it is not possible to draw explain why. B. a rhombus that is not a square. Possible answer: The figure has four congruent sides but no right angles.

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