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8.1 Quadrilaterals

8.1 Quadrilaterals. Quadrilaterals. § 8.1 Quadrilaterals. § 8.2 Parallelograms. § 8.3 Tests for Parallelograms. § 8.4 Rectangles, Rhombi, and Squares. § 8.5 Trapezoids. Vocabulary. Quadrilaterals. What You'll Learn.

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8.1 Quadrilaterals

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  1. 8.1 Quadrilaterals

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

  3. Vocabulary Quadrilaterals What You'll Learn You will learn to identify parts of quadrilaterals and find thesum of the measures of the interior angles of a quadrilateral. 1) Quadrilateral 2) Consecutive 3) Nonconsecutive 4) Diagonal

  4. Quadrilaterals four four A quadrilateral is a closed geometric figure with ____ sides and ____ vertices. The segments of a quadrilateral intersect only at their endpoints. Special types of quadrilaterals include squares and rectangles.

  5. Quadrilaterals Quadrilaterals are named by listing their vertices in order. There are several names for the quadrilateral below. Some examples: quadrilateral ABCD B quadrilateral BCDA A quadrilateral CDAB or quadrilateral DABC D C

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

  7. Q P S R Quadrilaterals Segments that join nonconsecutive vertices of a quadrilateral are called________. diagonals R and P arenonconsecutivevertices. S and Q arenonconsecutivevertices.

  8. Q T R S Quadrilaterals Name all pairs of consecutive sides: Name all pairs of nonconsecutive angles: Name the diagonals:

  9. A B D C 360 Quadrilaterals Considering the quadrilateral to the right. 1 What shapes are formed if a diagonal is drawn? ___________ two triangles 2 3 5 4 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 6 180 Find m1 + m2 + m3 + m4 + m5 + m6 + 180 This leads to the following theorem.

  10. b° a° c° d° Quadrilaterals 360 360 a + b + c + d =

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

  12. Quadrilaterals End of Section 8.1

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