Chapter 8: Quadrilaterals
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1 Chapter 8: Quadrilaterals Date Lesson Lesson Assignment Fri 10/ Find Angle Measures in Polygons p. 510 #(3-21,39-47)all Mon 10/ Use Properties of Parallelograms Prove Quadrilaterals are Parallelograms Section WS Tue 10/ Quiz Use Properties of Rhombuses, Rectangles, and Squares p. 537 #(1-25)odd, (26-29,32-37)all (66-70)all Wed 10/ Use Properties of Trapezoids and Kites p. 546 #(7-27,45,46)all Thu 11/1 8.6 Identify Special Quadrilaterals Section 8.6 Worksheet Fri 11/2 Quiz Test Review Practice Test Mon 11/3 TEST Chapter 8 Test (150 points) Notes: *Tutoring is after school Monday, Wednesday, and Friday from 2:35-3:35pm *I am available during both lunches for help as well. *All assignments subject to change. *If you are absent, check the Absent board for any changes. Write absent at the top of your work and turn into the Absent basket. Geometry Chapter 8 Notes - page 1
2 8.1 Find Angle Measures in Polygons Draw examples of 3-sided, 4-sided, 5-sided, and 6-sided convex polygons. In each polygon, draw all the diagonals from one vertex. Notice that this divides each polygon into triangular regions. Polygon Triangle Quadrilateral Pentagon Hexagon Number of Sides Number of Triangles Sum of Interior Angles Theorem 8.1: Polygon Interior Angles Theorem The sum of the measures of the interior angles of a convex n-gon is: Corollary to Thm 8.1: Interior Angles of a Quadrilateral The sum of the measures of the interior angles of a quadrilateral is. Ex 1: a) Find the sum of the measures of the interior angles of a do-decagon and a 20-gon. b) Find x. Geometry Chapter 8 Notes - page 2
3 Ex 2: The sum of the measures of the interior angles of a convex polygon is given. Classify the polygon by the number of sides. a) 360 b) 1440 c) 5040 In the following diagrams, find each exterior angle. Then find the sum of the exterior angles. What pattern do you notice? Theorem 8.2: Polygon Exterior Angles Theorem The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is: Ex 3: a) Find the sum of the measures of the exterior angles of a do-decagon and a 20-gon. b) Find x in each figure. Geometry Chapter 8 Notes - page 3
4 Question: What does it mean to be a regular polygon? Sum Each angle of a Regular Polygon Interior Angles Exterior Angles Ex 2: Find x. a) b) c) d) What is the measure of each interior angle and exterior angle of a regular decagon? e) Find x. f) The measures of the interior angles of a quadrilateral are x,3 x,5 x, and 6x. What is the measure of the largest angle? Geometry Chapter 8 Notes - page 4
5 Properties of Parallelograms Prove Quadrilaterals are Parallelograms Definition of a Parallelogram O N L M Properties of the Parallelogram A quadrilateral is a parallelogram if and only if.. opposite sides are congruent. O N L M opposite angles are congruent. O N L M consecutive angles are supplementary. O N L M diagonals bisect each other. O N L M one pair of opposite sides are congruent & parallel. O N L M Geometry Chapter 8 Notes - page 5
6 Ex 1: Find the value of each variable in the parallelogram. a) b) c) d) e) f) Ex 2: ABCD is a parallelogram. Find the lengths and angle measures. a) m ADC b) m BCD c) m BEC d) m BCE 115 e) m ADB f) m BCE Geometry Chapter 8 Notes - page 6
7 Ex 3: Are you given enough information to determine whether the quadrilateral is a parallelogram? Explain. a) b) c) Quadrilateral ABCD, with AB CD, and BC= 8, AD= 8 d) e) f) JMK LKM Ex 4: Using Algebra What values of x and y will make the quadrilateral a parallelogram? a) b) c) Geometry Chapter 8 Notes - page 7
8 8.4 Rhombuses, Rectangles, and Squares Definition of a Rhombus Definition of a Rectangle Definition of a Square Theorems Parallelograms RHOMBUS RECTANGLE SQUARE Geometry Chapter 8 Notes - page 8
9 Ex 1: a) b) Decide if the statement is sometimes, always, or never true. a. A rectangle is a parallelogram. b. A square is a rectangle. c. A parallelogram is a rhombus. c) Name each quadrilateral parallelogram, rectangle, rhombus, and square for which the statement is true. a. It is equilateral. b. The diagonals are congruent. c. It can contain obtuse angles. d. It contains no acute angles. Ex 2: Classify the special quadrilateral. Explain your reasoning. Then find the values of x and y. a) b) Geometry Chapter 8 Notes - page 9
10 Ex 3: Use properties of special quadrilaterals to find the value of x or y. a) ABCD is a rhombus. b) EFGH is a rectangle. c) DEFG is a rhombus.. Ex 4: The diagonals of rectangle WXYZ intersect at P. Given that m YXZ = 50 and XZ = 12, find the indicated measure. a) m WXZ b) m WPX c) WY d) PY d) WX Geometry Chapter 8 Notes - page 10
11 8.5 Trapezoids and Kites Definition of a Trapezoid Base Angles: Definition of an Isosceles Trapezoid Properties of Isosceles Trapezoid A trapezoid is isosceles if and only if. each pair of base angles are congruent diagonals are congruent Ex 1: Find the angle measures of ABCD. a) b) c) Geometry Chapter 8 Notes - page 11
12 Midsegment of a Trapezoid The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases. Ex 1: Using Trapezoids The midsegment of the trapezoid is RT. Solve for x. a) e) f) Definition of a Kite Properties of a Kite If a quadrilateral is a kite, then. diagonals are perpendicular exactly one pair of opposite angles are congruent Ex 2: Using Kites Find the length of the sides to the nearest tenth or the measure of the angles in the kite KITE. a) b) c) d) Geometry Chapter 8 Notes - page 12
13 8.6 Summarizing All Quadrilaterals Points A, B, C, and D are vertices of a quadrilateral. a. Plot the coordinates of the quadrilateral. b. Give the most specific name for the quadrilateral. c. Justify your answer using the slope, distance and/or midpoint formulas. 1 A a. b. B C c. D 2. A a. b. B C c. D Geometry Chapter 8 Notes - page 13
14 3. A a. b. B C c. D 4. A a. b. B C c. D Geometry Chapter 8 Notes - page 14
15 ISOSCELES TRAPEZOID Geometry Chapter 8 Notes - page 15
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