Exam 16: Polygons

For the following conjecture, draw an example that supports the claim and also one that shows the claim is false. "The diagonals of a parallelogram are equal."

If a polygon is equiangular, then it must be:

Indicate whether each statement is always true, sometimes true, or never true. If the answer is sometimes true, then draw a picture of a shape that meets both requirements and a shape that meets only the first requirement. A) A parallelogram is a rectangle. B) A rectangle is a parallelogram. C) A rhombus is a rectangle. D) A prism is a pyramid.

State two facts that are true for the diagonals of every rhombus.

Sketch an example of each description if it is possible. If any sketches are not possible, explain why. A) an equilateral quadrilateral that is not equiangular (What is this shape usually called?) B) an equilateral obtuse triangle C) a pentagon with exactly three right angles

Consider the following definitions of a trapezoid. Definition A: A quadrilateral with at least one pair of opposite sides parallel. Definition B: A quadrilateral with exactly one pair of opposite sides parallel. Is it possible to draw a figure that is a trapezoid according to definition A but not a trapezoid according to definition B? If yes, draw a figure that satisfies the conditions and explain why your figure satisfies those conditions. If no, explain why not.

An isosceles triangle has two angles that measure 100° and 40°. How large is the third angle?

Every trapezoid is a special parallelogram.

A rhombus is a kite.

Give the best name (if the shape is possible) for the descriptions listed below. If the shape is not possible, explain why. A) a kite that is also an isosceles trapezoid B) a rhombus that is not equilateral C) an equilateral (but not regular) isosceles trapezoid

Draw (if possible) a kite that does not have four congruent sides. If it is not possible, explain why.

A pentagonal pyramid has a total of five vertices.

Complete the following statements. A) The measure of EACH interior angle of a regular decagon is _____. B) If an interior angle of a regular polygon is 175°, then the polygon has _____ sides. C) The number of congruent sides on a scalene triangle is _____. D) The number of diagonals in a 16-gon is _____.

Fill in each blank with the BEST choice from the list of shapes A-E. You may re-use a choice. _______has parallel lateral edges _______a regular quadrilateral _______has an equal number of faces and vertices _______a polygon that is never a kite _______possibility of all its faces being regular is always a kite _______has lateral faces that are triangular regions has two bases A) pyramid B) non-square rectangle C) parallelogram D) square E) oblique prism

Any fact that is true for every rectangle is also true for every quadrilateral.

Every square is a special quadrilateral.

An angle that is supplementary to an angle with size 70° has what size?

Why is it NOT safe to make a general conclusion based on a drawing?