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Quadrilaterals § 8.1 Quadrilaterals 8.1 Quadrilaterals § 8.4 Rectangles, Rhombi, and Squares 8.4 Rectangles, Rhombi, and Squares § 8.3 Tests for Parallelograms 8.3 Tests for Parallelograms § 8.2 Parallelograms 8.2 Parallelograms § 8.5 Trapezoids 8.5 Trapezoids

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Quadrilaterals Yo u will le arn to   ide ntify parts  o f q uadrilate rals   and  find the s um  o f the  m e as ure s  o f the  inte rio r ang le s  o f a  q uadrilate ral. 1)  Q uadrilate ral 2)  C o ns e c utive 3)  No nc o ns e c uti ve 4)  Diag o nal
Quadrilaterals A quadrilateral is a closed geometric figure with ____ sides and ____ vertices. four four The segments of a quadrilateral intersect only at their endpoints. Quadrilaterals Not Quadrilaterals Special types of quadrilaterals include s q uare s and re c tang le s .

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S R Q P Quadrilaterals Any two _______ of a quadrilateral are either __________ or _____________. consecutive nonconsecutive sides vertices angles

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Quadrilaterals S R Q P Segments that join nonconsecutive vertices of a quadrilateral are called ________. diag o n als S and Q are nonconsecutive vertices. diagonal a is SQ R and P are diagonal a is RP
Quadrilaterals Q T S R Name all pairs of consecutive sides: Name all pairs of nonconsecutive angles: Name the diagonals: RS and QR ST and RS TQ and ST QR and TQ S and Q R and T and QS TR

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Quadrilaterals D C B A Considering the quadrilateral to the right. What shapes are formed if a diagonal is drawn? ___________ two   triang le s 1 2 3 4 5 6 Use the Angle Sum Theorem (Section 5-2) to find m 1 + m 2 + m 3 180 Use the Angle Sum Theorem (Section 5-2) to find m 4 + m 5 + m 6 180 Find m 1 + m 2 + m 3 + m 4 + m 5 + m 6 180 + 180 360 This leads to the following theorem.
Quadrilaterals Theorem 8-1 The sum of the measures of the angles of a quadrilateral is ____. 360 a ° d ° c ° b ° a + b + c + d = 360

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Quadrilaterals A D C B m A + m B + m C + m D = 360 x + 2x + x – 10 + 50 = 360 Find the measure of B in quadrilateral ABCD if A = x, B = 2x, C = x – 10, and D = 50. 4x + 40 = 360 4x = 320 x = 80 B = 2x B = 2(80) B = 160

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Parallelograms Yo u will le arn to  ide ntify and us e  the   pro pe rtie s  o f  paralle lo g ram s .
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