8.1 Quadrilaterals

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

You will learn to identify parts of quadrilaterals and find the sum of the measures of the interior angles of a quadrilateral. 1) Quadrilateral 2) Consecutive 3) Nonconsecutive 4) Diagonal

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

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

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

S R Q P Segments that join nonconsecutive vertices of a quadrilateral are called ________. diagonals S and Q are nonconsecutive vertices. R and P are nonconsecutive vertices.

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

D C B A Considering the quadrilateral to the right. What shapes are formed if a diagonal is drawn? ___________ two triangles Use the Angle Sum Theorem (Section 5-2) to find m  1 + m  2 + m  Use the Angle Sum Theorem (Section 5-2) to find m  4 + m  5 + m  Find m  1 + m  2 + m  3 + m  4 + m  5 + m  This leads to the following theorem.

Theorem 8-1 The sum of the measures of the angles of a quadrilateral is ____. 360 a°a° d°d° c°c° b°b° a + b + c + d = 360

A D C B m  A + m  B + m  C + m  D = 360 x + 2x + x – = 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