Figure 1: Triangle Review

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Presentation transcript:

Figure 1: Triangle Review Triangle Types Name Property Angle Angle Sum of Interior Angles =_______ degrees for a triangle Interior + Exterior angle =_______ degrees for a triangle

Figure 2: Interior / Exterior Angles Draw and label an exterior angle and interior angle for each figure

Figure 3: Interior Triangles Draw and label all interior angles for each figure (both the quadrilaterals and the triangles) Each quadrilateral has __________ triangles inside For each quadrilateral, the sum of the interior angles equals _______ degrees What is the relationship between the number of triangles and the sum of the interior angles? __________________________________________________

Figure 4: Interior Triangles Draw interior triangles for each polygon starting from the same vertex each time. Draw all interior angles for both the polygon and the triangles

Total number of degrees Figure 5: Activity Fill in the blanks in column 1 (number of sides) Fill in rows 2 through 7 for column 2 (Number of triangles), and column three (Total number of degrees) Try to determine a general formula (last two rows) ID Number of sides Number of triangles Total number of degrees 1 3 (Triangle) 180 2 4 (Quadrilateral) 3 5 (_____agon) 4 6 (_____agon) 5 7 (_____agon) 6 8 (_____agon) 7 10 (____agon) 8 100 9 N

Figure 5a: Guided Practice Find the sum of the interior angles for each figure (feel free to use the triangle method). 3 2 1 4 Confirm your answer to 2 and 3 by using a protractor (record each angle measured) Please write the formula for determining the sum of the interior angles of a polygon: Sum = ____________ Please re-write the formula as a sentence __________________________________________________ If the sum of the interior angles of a polygon is 1620 deg, how many sides does it have? _________ For an infinite sided polygon, what is the sum of the interior angles?__________ What is another name for an infinite sided polygon?___________

Figure 6: Summation Baseline questions (all must answer) 1. What are the sums of the interior angles for any polygon (formula)? 2. Does the answer change if the polygon is regular or irregular? Homework Problem 3. Does the answer change if the polygon has a concave angle? (Show example to support your answer)

Figure 7: Quiz 1. Draw and label an exterior angle and interior angle for each polygon below 2. Determine the number of triangles that will fit into each polygon above 3. Determine the sum of the interior angles for each polygon above 4. Write a general formula for the sum of the interior angles for a polygon 5. Does the formula change for regular vs irregular convex polygons?