7-3 Parallel and Perpendicular Lines
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1 7-3 Parallel and Perpendicular Lines Interior Angles: Exterior Angles: Corresponding Angles: Vertical Angles: Supplementary Angles: Complimentary Angles:
2 7-3 Parallel and Perpendicular Lines Interior Angles: Exterior Angles: 3, 4, 5, 6 1, 2, 7, 8 Corresponding Angles: & 5, 3 & 7; 2 & 6; 4 & 8 Vertical Angles: 1 & 4, 2 & 3, 5 & 8, 6 & 7 Supplementary Angles: Complimentary Angles: 1 & 3, 2 & 4, 5 & 7, 6 & 8, 1 & 2, 3 & 4, 5 & 6, 7 & 8 None
3 7-3 Parallel and Perpendicular Lines Draw this on your paper. Fill in the rest of the angle measures
4 7-4 Circles Learn to identify parts of a circle and to find central angle measures.
5 7-4 Circles Insert Lesson Title Here circle center of a circle radius diameter chord arc central angle Sector Pi Π Vocabulary
6 7-4 Circles A circle is the set of all points in a plane that are the same distance from a given point, called the center of a circle. A circle is named by its center. For example, if point A is the center of a circle, then the name of the circle is circle A. There are special names for the different parts of a circle.
7 7-4 Circles Arc Part of a circle named by its endpoints Radius Line segment whose endpoints are the center of a circle and any point on the circle Diameter Line segment that passes through the center of a circle, and whose endpoints lie on the circle Chord Line segment whose endpoints are any two points on a circle. Can go through the center.
8 7-4 Circles Additional Example 1: Identifying Parts of a Circle Name the parts of circle M. A. radii MN, MR, MQ, MO N O B. diameters NR, QO P M Q C. chords NR, QO, QN, NP R Reading Math Radii is the plural form of radius.
9 7-4 Circles Try This: Example 1 Name the parts of circle M. B A. radii GB, GA, GF, GD A C B. diameters C. chords BF, AD AH, AB, CE, H F G E D BF, AD
10 7-4 Circles Sector A central angle of a circle is an angle formed by two radii. A sector of a circle is the part of the circle enclosed by two radii and an arc connecting them. (PIZZA) The sum of the measures of all of the central angles in a circle is 360. We say that there are 360 in a circle. ) Central angle
11 7-4 Circles Additional Example 2: Problem Solving Application The circle graph shows the results of a survey about favorite types of muffins. Find the central angle measure of the sector that shows the percent of people whose favorite type of muffin is blueberry.
12 7-4 Circles 2 Make a Plan There are 360 in a circle. Since the sector is 40% of the circle graph, the central angle is 40% of the 360 in the circle. 40% of 360 = Solve Additional Example 2 Continued = 144 Multiply. The central angle of the sector is 144.
13 7-4 Circles Additional Example 2 Continued 4 Look Back The 40% sector is less than half the graph, and 144 is less than half of 360. Therefore, the answer is reasonable.
14 8-3 Perimeter and Circumference The Pi Song
15 7-4 Circles Circumference C=Πd or C=2Πr Π= 3.14 To find the Circumference, multiply the diameter times Π (3.14) or Multiply the radius times 2 times Π (3.14)
16 7-4 Circles Circumference C=Πd Find the circumference of the circle with radius 3 mm. 3 mm C = Π d C = C = mm
17 7-4 Circles Area A=Πr² Find the area of the circle with diameter 4 cm. 4 cm A = Π r ² A = ² A = A = cm²
18 7-5 Polygons Learn to identify and name polygons.
19 7-5 Polygons Insert Lesson Title Here Vocabulary polygon side vertex of a polygon regular polygon
20 7-5 Polygons Triangles and rectangles are examples of polygons. A polygon is a closed plane figure formed by three or more line segments. Each line segment forms a side of the polygon, and meets, but does not cross, another line segment at a common point. This common point is a vertex of a polygon. Side The polygon at left has six sides and six Vertex vertices. Remember! Vertices is plural for vertex.
21 7-5 Polygons Additional Example 1A & 1B: Identifying Polygons Determine whether each figure is a polygon. If it is not, explain why not. A. B. The figure is a polygon. It is a closed figure with 4 line segments. The figure is not a polygon. It is not a closed figure.
22 7-5 Polygons Additional Example 1C & 1D: Identifying Polygons Determine whether each figure is a polygon. If it is not, explain why not. C. D. The figure is not a polygon. The figure is not formed by line segments. The figure is not a polygon. There are line segments in the figure that cross.
23 7-5 Polygons Try This: Example 1C & 1D Determine whether each figure is a polygon. If it is not, explain why not. C. D. The figure is not a polygon. The figure is not formed by line segments. The figure is not a polygon. There are line segments in the figure that cross.
24 7-5 Polygons Polygons are classified by the number of sides and angles they have. Triangle 3 sides 3 angles Quadrilateral 4 sides 4 angles Pentagon 5 sides 5 angles Hexagon 6 sides 6 angles Heptagon 7 sides 7 angles Octagon 8 sides 8 angles Nonagon 9 sides 9 angles Decagon 10 sides 10 angles
25 7-5 Polygons Additional Example 2: Classifying Polygons Name each polygon. A. B. Octagon Quadrilateral
26 7-5 Insert Polygons Lesson Title Here Name each polygon. Try This: Example 2 A. B. Quadrilateral Pentagon
27 7-5 Insert Polygons Lesson Title Here A regular polygon is a polygon in which all sides are congruent and all angles are congruent.
28 7-5 Polygons Additional Example 3: Identifying and Classifying Regular Polygons Name each polygon and tell whether it is a regular polygon. If it is not, explain why not. A. B. The figure is a regular quadrilateral. A regular quadrilateral is also called a square. The figure is a quadrilateral. It is not a regular polygon because all of the sides are not congruent.
29 7-5 Insert Polygons Lesson Title Here Try This: Example 3 Name each polygon and tell whether it is a regular polygon. If it is not, explain why not. A. B. The figure is a triangle. It is not a regular polygon because all sides and angles are not congruent. The figure is a regular triangle.
30 7-5 Polygons Insert Lesson Title Here Lesson Quiz Determine whether each statement is true or false. 1. Every polygon is a closed figure. true 2. Every open figure is a polygon. false 3. A pentagon with sides lengths of 10 units and angles measuring 108 is a regular polygon. true 4. A quadrilateral with side lengths of 10, 12, 10, and 12 units is a regular polygon. false 5. What is the name of a five-sided polygon? pentagon
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