Module 71 Interior and Exterior Angles Today you will need your Notes A blank piece of paper 2 3 1 180 Interior Angles of a Triangle Triangle Sum Theorem Proof 1 Take out your sheet of paper ID: 769157
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Module 7.1 – Interior and Exterior Angles Today you will need your: Notes A blank piece of paper
2 3 1 + = 180° Interior Angles of a Triangle
Triangle Sum Theorem – Proof #1 Take out your sheet of paper Fold and tear your paper until you make a triangle (or use your scissors) – any triangle will do Use your pen or pencil to put a small dot or circle in each of the corners of the triangleNow tear off the corners like the diagram below, and await instructions
Triangle Sum Theorem – Proof #2 Line l is parallel to segment AC What is the relationship between: , , and Supplementary and and Congruent (alternate interior angles!) Congruent (alternate interior angles!) , , and Supplementary
2 3 1 + = 180° Use the theorem to solve problems
2 3 1 = (x + 20)° = (3x + 5 )° = (6x + 25)° Use the theorem to find x
Homework Interior Angles of a Triangle, HW 1
Interior Angles of any Polygon Today you will need: Last night’s homework (take this out now for review) Your notes The polygon worksheet
Interior Angles of any Polygon 2 3 1 + = 180° Recall the Triangle Sum Theorem:
Interior Angles of any Polygon Now imagine two triangles back-to-back We now have a QUADRILATERAL!
Interior Angles of any Polygon + = 180° 2 1 3
Interior Angles of any Polygon + = 180° 2 1 3 5 6 4 + = 180°
Interior Angles of any Polygon + + = 2 1 3 5 6 4 360° A 4-sided polygon has an interior angle measure of 360°
Interior Angles of any Polygon Now take out your worksheet, and work with your neighbor to try to find the interior angles of other polygons. If you think you have a measure, come up to the chart on the smartboard and write in what you have found.
Polygon Chart Polygon Type Number of Sides Total Interior Angle Measure Triangle 3 Quadrilateral 4 Pentagon 5 Hexagon 6 Heptagon 7 Octagon 8 Decagon 10
Polygon Chart – the pattern Polygon Type Number of Sides The Pattern Total Interior Angle Measure Triangle 3 (3-2)*(180°) 180° Quadrilateral 4 (4-2)*(180°) 360° Pentagon 5 (5-2)*(180°) 540° Hexagon 6 (6-2)*(180°) 720° Heptagon 7 (7-2)*(180°) 900° Octagon 8 (8-2)*(180°) 1080° Decagon 10 (10-2)*(180°) 1440°
Interior Angles of any Polygon To find the sum of the interior measures of the angles of any polygon, subtract 2 from the total number of sides, and multiply that number by 180°
Interior Angles of any Polygon What is the total interior angle measure for a polygon of the following numbers of sides? 12 sides: 17 sides: 30 sides: 50 sides: 100 sides: 420 sides:
Interior Angles of any Polygon Regular Polygon: A polygon whose sides and angles are all the same measure.
Interior Angles of any Polygon Find the measure of one angle for the following regular polygons: Polygon Type Total Angle Measure Measure of EACH angle Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Decagon
Interior Angles of any Polygon - practice Find the value of ‘x’
Interior Angles of any Polygon - practice Find the value of ‘x’
Interior Angles of any Polygon - practice Find the value of ‘x’
Interior Angles of any Polygon - practice Find the value of ‘x’