Question 1

A pentagonal pyramid has a total of five vertices.

Accepted Answer

A pentagonal pyramid has a total of 6 vertices: 5 vertices at the base which is a pentagon, and 1 vertex at the apex.

Question 2

The lateral faces of a prism are always parallelogram regions.

Accepted Answer

The lateral faces of a prism are formed by connecting the corresponding vertices of the two polygonal bases with line segments, resulting in parallelogram regions due to the parallel and equal sides of these segments.

Question 3

A rhombus is a kite.

Accepted Answer

A rhombus is a special type of kite where all four sides are of equal length.

Question 4

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

Accepted Answer

The interior angles of any trapezoid, including an isosceles trapezoid, always add up to 360°.

Question 5

Give the best name for the following shapes.
A) a regular quadrilateral
B) an isosceles trapezoid with at least one right angle

Accepted Answer

The answer of Give the best name for the following...

Question 6

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

Accepted Answer

The answer of If possible, sketch an example of each...

Question 7

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."

Accepted Answer

The answer of For the following conjecture, draw an example...

Question 8

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

Accepted Answer

A rectangle has all the properties of an isosceles trapezoid, including one pair of parallel sides and congruent base angles.

Question 9

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

Accepted Answer

The answer of Why is it NOT safe to make...

Question 10

Why is a result from inductive reasoning NOT completely trustworthy?

Accepted Answer

The answer of Why is a result from inductive reasoning...

Question 11

Put the following terms in the blanks below to show the relationship among them: isosceles trapezoid, parallelogram, quadrilateral, rectangle, and rhombus.

Accepted Answer

The answer of Put the following terms in the blanks...

Question 12

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

Accepted Answer

The answer of Arrange (only) the following terms in a...

Question 13

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 _____.

Accepted Answer

The answer of Complete the following statements.
A) The measure of...

Question 14

For each shape, sketch an example if it is possible. (Be sure to mark your picture to fit.) If it is impossible, say so and explain why or show a counterexample.
A) a parallelogram with exactly one right angle
B) an isosceles right triangle
C) a rectangle that is not a parallelogram
D) an equilateral quadrilateral that is not regular
E) a concave hexagon

Accepted Answer

The answer of For each shape, sketch an example if...

Question 15

Match between columns Premises: Any fact that is true for every parallelogram is also true for every square. The diagonals of a rhombus are congruent.
Every rhombus is a kite.
The opposite angles of a parallelogram are congruent.
Every equilateral triangle is an isosceles triangle.
Any fact that is true for every rectangle is also true for every quadrilateral.
Every rectangle is a square. The diagonals of a rectangle bisect each other. Every square is a quadrilateral. Every trapezoid is a parallelogram.

Accepted Answer

The Answer of False and True is...

Question 16

A student states that a square cannot be a rhombus. What irrelevant characteristic(s) might she be assuming to be important? How would you help her to understand her error?

Accepted Answer

The answer of A student states that a square cannot...

Question 17

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

Accepted Answer

The answer of How many diagonals does each of these...

Question 18

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?

Accepted Answer

The answer of The sizes of three interior angles of...

Question 19

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

Accepted Answer

The answer of An isosceles triangle has two angles that...

Question 20

If a polygon is equiangular, then it must be:

Accepted Answer

The answer of If a polygon is equiangular, then it...

Quiz 16: Polygons

A pentagonal pyramid has a total of five vertices.

The lateral faces of a prism are always parallelogram regions.

A rhombus is a kite.

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

Give the best name for the following shapes. A) a regular quadrilateral B) an isosceles trapezoid with at least one right angle

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

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."