Exam 16: Polygons

If possible, sketch an example of each description. If it is not possible, explain why. Use tick marks and hidden edges and label equal angles to make your intent clear. A) a trapezoid with exactly two right angles B) a kite with equal diagonals

Sketch, if possible, an obtuse isosceles triangle that has an angle with 30°. If such a triangle exists, give the measures of the other angles. If such a triangle is impossible, explain why.

Create a Venn diagram or a hierarchy diagram for only the following terms: quadrilateral, square, rectangle, polygon, and rhombi.

A) How many different arrangements of three identical rhombi are possible in which each rhombus matches up edge to edge with at least one other rhombus? Two arrangements are considered the same if one of the arrangements can be flipped and/or rotated to obtain the other arrangement. Sketch all possible arrangements. B) Explain a counting strategy you used to justify that you have found all the different arrangements.

Tell whether each statement is always true, sometimes true, or never true. Justify your choice. A) The diagonals of a parallelogram bisect each other. B) The diagonals of a kite bisect each other.

Which shape will have ALL of the properties that every isosceles trapezoid has?

Sketch an example, if it is possible, of each shape described. If any are not possible tosketch, explain why. A) an isosceles triangle that is not an acute triangle B) a quadrilateral with two 90° angles that is not a rectangle (Be sure to mark the 90° angles.) C) a kite that is also a rectangle D) a triangular right prism (Show every hidden edge as a dashed segment.)

Arrange (only) the following terms in a hierarchical diagram, with the most general at the top: kite, square, polygon, trapezoid, and rectangle.

Which, if either, of the following is IMPOSSIBLE for x, y, and z in the sketch below? (The drawing is not to scale.) I. x = 100, y = 110, z = 150 II. x = 80, y = 130, z = 150

The diagonals of a parallelogram are equal.

Which statement is TRUE for every rhombus? I. The diagonals of a rhombus must be equal. II. The sides of a rhombus must be equal.

For each shape, sketch an example if it is possible. If it is not possible, say so and explain why. A) a trapezoid with exactly one right angle B) a parallelogram that is an isosceles trapezoid C) a pentagon with exactly one right angle D) an isosceles obtuse triangle E) a rhombus that is not a kite

If IJKLMN is a regular polygon, then:

The lateral faces of a prism are always parallelogram regions.

Draw (if possible) an isosceles trapezoid with exactly one right angle. If it is not possible, explain why.

The sizes of three interior angles of a quadrilateral are 65°, 35°, and 60°. What is the size of the fourth angle of the quadrilateral?

Every rectangle is a parallelogram.

A square is a rhombus.

The interior angles of a trapezoid add up to 360°, but only 270° if it is an isosceles trapezoid.

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