Quadrilaterals, Diagonals, and Angles of Polygons

A Polygon is a simple closed plane figure, having three or more line segments as sides A Quadrilateral is any four-sided closed plane figure A Diagonal a line segment that connects one vertex to another (but not next to it) on a polygon

Classifying Polygons Number of Sides Name of Polygon Number of Sides Name of Polygon 3Triangle4Quadrilateral 5Pentagon6Hexagon 7Heptagon8Octagon 9Nonagon10Decagon

Quadrilateral Angles We know that the interior angles of a triangle add up to 180 degrees How many degrees are in the interior angles of a quadrilateral?

Quadrilateral Angles If we draw a diagonal from one vertex across to the opposite vertex, we see that we have formed two triangles Therefore, the sum of two triangles will give you the measure of the interior angles of a quadrilateral = 360 degrees!

Quadrilateral Angles Checkpoint Find the missing angle of a quadrilateral with the following measures: m 1 = 117 m 2 = 110 m 3 = 75 m 4 = x = x = 360 x = 58

Angles of Polygons Mini-Lab Let’s explore this knowledge and how it relates to the angles of other polygons Copy and complete the table below: Number of SidesSketch of Figure Number of Triangles Sum of Angle Measurements 311(180) = (180) =

Angles of Polygons Mini-Lab Draw a pentagon with diagonals from one vertex to each opposing vertex

Angles of Polygons Mini-Lab Let’s explore this knowledge and how it relates to the angles of other polygons Copy and complete the table below: Number of SidesSketch of Figure Number of Triangles Sum of Angle Measurements 311(180) = (180) = (180) =

Angles of Polygons Mini-Lab Draw a hexagon with diagonals from one vertex to each opposing vertex

Angles of Polygons Mini-Lab Let’s explore this knowledge and how it relates to the angles of other polygons Copy and complete the table below: Number of SidesSketch of Figure Number of Triangles Sum of Angle Measurements 311(180) = (180) = (180) = (180) = 720 7

Angles of Polygons Mini-Lab Draw a heptagon with diagonals from one vertex to each opposing vertex

Angles of Polygons Mini-Lab Let’s explore this knowledge in how it relates to the angles of other polygons Copy and complete the table below: Number of SidesSketch of Figure Number of Triangles Sum of Angle Measurements 311(180) = (180) = (180) = (180) = (180) = 900

Angles of Polygons Mini-Lab What patterns do you see as a result of our experiment? The number of triangles in any polygon is always two less than the number of sides. Therefore, if n = the number of sides of the polygon; the sum of interior angles of any polygon can be expressed as (n – 2)180!

Angles of Polygons Checkpoint Find the sum of the measures of the interior angles of each polygon: 15-gon?23-gon?30-gon? (15-sided figure)(23-sided figure)(30-sided figure) 13 x 180 = 2340

Angles of Polygons Checkpoint Find the sum of the measures of the interior angles of each polygon: 15-gon?23-gon?30-gon? (15-sided figure)(23-sided figure)(30-sided figure) 13 x 180 = x 180 = 3780

Angles of Polygons Checkpoint Find the sum of the measures of the interior angles of each polygon: 15-gon?23-gon?30-gon? (15-sided figure)(23-sided figure)(30-sided figure) 13 x 180 = x 180 = x 180 = 5040

Regular Polygons A regular polygon is one that is equilateral (all sides congruent) and equiangular (all angles congruent) Polygons that are not regular are said to be irregular If the formula for finding the sum of measures of interior angles of a polygon is (n-2)180, how would you find the measure of each angle of a regular polygon? ( n – 2 )180 n

Regular Polygons Checkpoint Find the sum of the measures of the interior angles of each regular polygon and the measure of each individual angle: 15-gon?23-gon?30-gon? (15-sided figure)(23-sided figure)(30-sided figure) 13 x 180 = / 15 = 156

Regular Polygons Checkpoint Find the sum of the measures of the interior angles of each regular polygon and the measure of each individual angle: 15-gon?23-gon?30-gon? (15-sided figure)(23-sided figure)(30-sided figure) 13 x 180 = / 15 = x 180 = / 23 =

Regular Polygons Checkpoint Find the sum of the measures of the interior angles of each regular polygon and the measure of each individual angle: 15-gon?23-gon?30-gon? (15-sided figure)(23-sided figure)(30-sided figure) 13 x 180 = / 15 = x 180 = / 23 = x 180 = / 30 = 168

Homework Skill 4: Polygons (both sides) 6-3 Skills Practice: Polygons and Angles DUE TOMORROW!