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Lesson Menu Five-Minute Check (over Lesson 11–3) Then/Now New Vocabulary Key Concept: Angles of a Quadrilateral Example 1: Find Angle Measures Example 2: Real-World Example: Classify Quadrilaterals

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Over Lesson 11–3 5-Minute Check 1 Choose the figure after a 180° clockwise rotation about point S. A. B. C. D.

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Over Lesson 11–3 5-Minute Check 2 Choose the figure after a 270° clockwise rotation about point A. A. B. C. D.

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Over Lesson 11–3 5-Minute Check 3 Which figure does not have rotational symmetry? A. B. C. D.

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Over Lesson 11–3 5-Minute Check 4 A.A'(0, 3), B'(–6, 5), C'(1, 5) B.A'(0, 3), B'(5, 1), C'(–2, 1) C.A'(0, 3), B'(6, 5), C'(2, 4) D.A'(0, 3), B'(–5, 1), C'(2, 1) A triangle has vertices A(0, 3), B(–2, –3), and C(–2, 4). If the triangle is rotated clockwise 90° about point A, what are the new coordinates of the triangle?

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Then/Now You found missing angle measures of a triangle. (Lesson 10–3) Find missing angle measures of a quadrilateral. Classify quadrilaterals.

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Vocabulary quadrilateral

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Concept

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Example 1 Find Angle Measures ALGEBRA Find the value of x in the quadrilateral. Then find each missing angle measure. The sum of the measures of the angles is 360°. Let m Q, m R, m S, and m T represent the measures of the angles.

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Example 1 Find Angle Measures m Q + m R + m S + m T=360Angles of a quadrilateral x x=360Substitution 5x + 185=360Combine like terms. 5x – 185=360 – 185Subtract 185 from each side. 5x=175Simplify. x=35Divide each side by 5. Answer: So, m T = 35° and m R = 4(35) or 140°.

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Example 1 A.x = 4; m A = 4° and m C = 16° B.x = 5; m A = 5° and m C = 20° C.x = 40; m A = 40° and m C = 160° D.x = 104; m A = 104° and m C = 416° Find the value of x. Then find each missing angle measure.

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Example 2 Classify Quadrilaterals Answer: parallelogram Classify the quadrilateral shown using the name that best describes it. The quadrilateral has both pairs of opposite sides parallel and congruent.

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Example 2 A.square B.rectangle C.rhombus and rectangle D.parallelogram and square QUILT PATTERN The figure shows a pattern for the border of a quilt. Classify the quadrilaterals used to form the flower and the leaves using the name that best describes them.

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End of the Lesson

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