Exam 16: Polygons

It is possible to make a regular pyramid using an isosceles trapezoid as a base.

Every trapezoid is a special parallelogram.

The sum of the measures of all of the angles of a 17-gon is _____.

State a fact that is true for all rectangles but not true for all parallelograms.

There are a total of 1175 diagonals in a 50-gon.

How many diagonals does each of these shapes have? A) a pentagon B) a 103-gon

Why is 10 called a triangular number?

Every rhombus is a parallelogram.

State two facts that are true for every parallelogram.

The diagonals of every parallelogram:

What is the sum of the measures of the exterior angles, one at each vertex, of every convex polygon? Explain your reasoning.

Every rectangle is a special square.

Every rectangle is a parallelogram.

State a fact that is true for all rhombi but not true for all kites.

Every kite is also a parallelogram.

Any fact that is true for every parallelogram is also true for every square.

Draw a tree diagram showing the hierarchy of the following quadrilaterals: kites, trapezoids, parallelograms, squares, rhombuses, isosceles trapezoids, and rectangles. (Note: Use "quadrilaterals" at the top of your diagram.)

Every square is a special quadrilateral.

Every rectangle is a special square.

When asked to find the sum of the interior angles in a hexagon, a student writes the statement alongside the sketch below. Comment on whether the student's mathematical reasoning is correct or incorrect. If it is correct, explain how you know. If it is incorrect, explain what was incorrect about the student's thinking and what he/she would have to do to correct the error.