Unit 5 Lesson 1 Polygons and Angle Measures I. What is a polygon? (Page 322) A polygon is a figure that meets the following conditions: It is formed by or more segments called, such that no two sides with a common endpoint are collinear. Each side intersects exactly two other sides, one at each endpoint, called a of the polygon. Polygons are named by the number of sides they have: Number of sides 3 4 7 8 10 n Name of the polygon Pentagon Hexagon Nonagon Undecagon Dodecagon Figures,, are polygons. Figure is not a polygon because. Figure is not a polygon because. Figure is not a polygon because.
II. Describing polygons (page 323) A polygon is if no line that contains a side of the polygon contains a point in the interior of the polygon. A polygon that is not convex is called or. Example 1: Identify the polygon and state whether it is convex or concave. A polygon is if all of its sides are congruent. A polygon is if all of its interior angles are congruent. A polygon is if it is equilateral and equiangular. Example 2: A of a polygon is a segment that joins two nonconsecutive vertices.
III. Interior Angle Measures of a Polygon (page 662-663) These are worth memorizing!!!! All 3 interior angles of a triangle add to All 4 interior angles of a quadrilateral add to For all other polygons: The sum of the measures of the interior angles of a convex n- gon is. (where n represents the number of sides) (a) (b) (c) (d)
IV. Exterior Angle Measures of a Polygon An exterior angle of a polygon is found by extending the sides of the polygon. Each interior angle forms a linear pair with each exterior angle. Note: A polygon with n sides will have n interior angle and n exterior angles. Example of a pentagon s exterior angles The sum of the measures of the exterior angles of a convex polygon will always be Example 1: Find the value of x in the diagram. Example 2: Find the value of x and y in the diagram.
Unit 5 Lesson 2 Properties of Parallelograms Definition: Parallelogram Properties/Theorems: (about sides, angles, and diagonals) List each property and include a diagram for each. Property Diagram 1. 2. 3. 4.
Using the Properties of a Parallelogram: Example 1: Example 2: Example 3: Find the missing measurements. m D = EH = y = x =
Unit 5 Lesson 3 Proving a Quadrilateral is a Parallelogram Describe the 6 ways to prove that a quadrilateral is a parallelogram: (see concept summary on page 340)
page 341 example 4 Show that A(2, - 1), B(1, 3), C(6, 5), and D(7, 1) are the vertices of a parallelogram. Method 1: Use the definition of a parallelogram to show that BOTH sets of opposite sides are parallel. Method 2: Use the property that BOTH sets of opposite sides of a parallelogram are congruent. Method 3: Use the combination theorem that ONE set of opposite sides are parallel AND congruent.
Unit 5 Lesson 4 Special Parallelograms Rhombus Definition: Rhombus Properties/Theorems: (include all parallelogram properties also) Property Diagram 1. 2. 3. 4. 5. 6.
Rectangle Definition: Rectangle Properties/Theorems: (include all parallelogram properties also) Property Diagram 1. 2. 3. 4. 5.
Square Definition: Square Properties/Theorems: (include all properties for parallelograms, rectangles, and squares) Property Diagram 1. 2. 3. 4. 5. 6. 7.
Unit 5 Lesson 5 Trapezoids/Kites Trapezoid definition: Isosceles Trapezoid definition: Properties/Theorems of isosceles trapezoids: Property Diagram 1. 2. Definition of a Midsegment: Midsegment Theorem:
Kite Definition: Kite Properties/Theorems: Property Diagram 1. 2.
Unit 5 Lesson 6 Comparing Quadrilaterals Example 1: Determine whether the quadrilateral is a parallelogram, trapezoid, rectangle, rhombus or square. The diagram shows CE EA and DE EB, so. This makes the quadrilateral a, so it cannot be a trapezoid! You cannot conclude that ABCD is a rectangle, rhombus, or square because no information about sides or angles given. Example 2: Are you given enough information in the diagram to conclude that ABCD is a square? Explain your reasoning. The diagram shows that all four are congruent. Therefore, you know that it is a. The diagram does not give any information about the angle measures, so you cannot conclude that ABCD is a square. Example 3: Identify the most specific quadrilateral. Explain. a. b. c. Example 4 a. What type of quadrilateral is ABCD? Explain. b. Is ABCD a square? Explain.
Unit 5 Lesson 7 Coordinate Proofs Using Slopes slopes show that segments are parallel or perpendicular. Parallel slopes are the same or equal Perpendicular slopes are opposite and reciprocals (slopes multiply to - 1) Using Distances distances show that segments are equal in length and therefore congruent. Pythagorean Theorem set up a right triangle by dropping a vertical a! + b! = c! segment from the highest point OR Distance Formula need two coordinate points d =!(x! x! )! + (y! y! )! Example 1: What type of quadrilateral is ABCD? Show work to support your answer.
Example 2: Is ORST a trapezoid? If so, is it isosceles? Show all work to support your answer.