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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 Lesson Menu

Choose the figure after a 180° clockwise rotation about point S. D. 5-Minute Check 1

Choose the figure after a 270° clockwise rotation about point A. D. 5-Minute Check 2

Which figure does not have rotational symmetry? B. C. D. 5-Minute Check 3

A triangle has vertices A(0, 3), B(–2, –3), and C(–2, 4) 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? 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) 5-Minute Check 4

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

quadrilateral Vocabulary

Concept

The sum of the measures of the angles is 360°. 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. Example 1

mQ + mR + mS + mT = 360 Angles of a quadrilateral Find Angle Measures mQ + mR + mS + mT = 360 Angles of a quadrilateral 75 + 4x + 110 + x = 360 Substitution 5x + 185 = 360 Combine like terms. 5x + 185 – 185 = 360 – 185 Subtract 185 from each side. 5x = 175 Simplify. x = 35 Divide each side by 5. Answer: So, mT = 35° and mR = 4(35) or 140°. Example 1

Find the value of x. Then find each missing angle measure. 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° Example 1

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

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. A. square B. rectangle C. rhombus and rectangle D. parallelogram and square Example 2

End of the Lesson