Exploration Monday: Polygons, Kites, Trapezoids

What is the relationship between the number of sides and the number of Diagonals joining A in a convex polygon?

What is the relationship between the number of sides and the number of triangles formed by the Diagonals joining A?

Using N to represent the number of sides, write the formula to calculate the SUM of the measures of all interior angles of a polygon.

What does this app reveal about the sum of the measures of the interior angles of a quadrilateral?

Does the shape of the quadrilateral make a difference? >> TRY different quadrilaterals by moving the vertices! [points A, B, C, or D]

Measure each interior angle. Add the angle measurements to find the sum for each polygon: >> Hint: click inside the polygon with the tool to measure all angles at once. (three answers required)

Calculate 180º•(N-2) for each polygon: (pentagon, hexagon, decagon) (three answers required)

Compare the results of Task 9 and Task 10 :

Measure an EXTERIOR ANGLE of the regular decagon. What is the sum of the measures of all 10 exterior angles of the decagon?

Does this result agree with the Polygon Exterior Angle-Sum Theorem?

Use the measure of an EXTERIOR angle in Task 13 to calculate the measure of one INTERIOR angle of the regular decagon.

Is your kite indestructible? (Can you neighbor "break" it?)

Is your trapezoid indestructible? (Can you neighbor "break" it?)

Create a conjecture about the opposite angles of a parallelogram:

Does the sum of the measures of the interior angles of a parallelogram also equal 360º ? >> Check your answer by measuring the interior angles on Task 20. using the tool.