Presentation on theme: "Polygons Where has Polly gone? Polygon A closed figure formed by joining three or more segments in a plane at their endpoints, with each line segment."— Presentation transcript:
Polygons Where has Polly gone?
Polygon A closed figure formed by joining three or more segments in a plane at their endpoints, with each line segment joining exactly 2 others. Each line segment is called a side of the polygon. This polygon has 8 sides.
Circle the figures that are polygons:
Why are these NOT polygons? A. Open side B. Curved side C. Vertex has more than 2 segments that meet D. Curved side
Vertex and diagonal A vertex is where 2 sides meet. A diagonal joins two nonconsecutive vertices. Name the vertices and the diagonal in this polygon: Vertices: A,B,C,D,E,F Diagonal: CE
List all the diagonals in this polygon: DB DA EC EB AC
Polygons are named by the number of sides.
Name these polygons: A. triangle B. Quadrilateral C. Pentagon D. Hexagon E. Octagon F. Dodecagon
Polygons with all sides and angles equal are regular polygons. Circle the regular polygons:
Polygons are named by naming consecutive vertices in order. Circle all the correct names for this polygon: pentagon ABCDE pentagon AEDCB pentagon ACDBE pentagon DCBAE pentagon BDCAE pentagon BAEDC
What is the sum of the angle measures in a triangle? Please draw a triangle on a piece of scratch paper. It can be any size or shape, just be sure it is a triangle.
Now, tear off the three angles of the triangle. Position the angles side-by-side on your desk. What shape do they make? Draw the angles side-by-side on your paper like this ↑
What is the measure of a straight line?
The sum of the angles of any triangle is 180° Find the measure of the missing angle: ے1 = (90 +35) ے1 = (125) ے1 = 55° 35° 90° ے1ے1
The sum of the angles of any triangle is 180° Find the measure of the missing angle: ے2 = ( ) ے2 = (130) ے2 = 50° 65° ے2ے2
Find x: 3x x x + 6 = 180 14x + 12 = 180 14x = 168 x = 12
What is the sum of the angle measures in a polygon? We can divide the polygon into triangles, then multiply the number of triangles by 180° How many triangles make up this quadrilateral? 2222 What is the sum of the angles of this quadrilateral? 2 x 180° = 360°
What is the sum of the angles in this hexagon? 4 x 180° = 720°
What is the sum of the angles in this pentagon? 3 x 180° = 540°
Do you HAVE to draw the triangles to find out how many of them there are in a polygon? NO! 4 sides,5 sides, 6 sides, 2 triangles 3 triangles 4 triangles n sides, n-2 triangles!
What is the sum of the measures of the angles of these polygons? 180(6-2)180(8-2)180(10-2) = 180(4)=180(6)= 180(8) = 720°= 1080°=1440°
Find the missing angle measure in this polygon: 180(5-2) = 180(3) = 540° 540° = X 540 = X 116° = X
Find the missing angle measure in this polygon: 180(9-2) = 180(7) = 1260° 1260° = X 1260 = X 121° = X