Advanced Geometry Concepts Quiz

1) Can a regular polygon exist?

I'm not sure

No

Maybe

Yes

A regular polygon is a polygon with all sides and angles being equal. Therefore, a regular polygon can indeed exist.

Explanation

A regular polygon is a polygon with all sides and angles being equal. Therefore, a regular polygon can indeed exist.

2) Two adjacent angles of a parallelogram are equal. What is the measure of each?

45 degrees

60 degrees

120 degrees

90 degree

In a parallelogram, opposite angles are equal and consecutive angles are supplementary. Therefore, if two adjacent angles are equal, they must each measure 90 degrees.

Explanation

In a parallelogram, opposite angles are equal and consecutive angles are supplementary. Therefore, if two adjacent angles are equal, they must each measure 90 degrees.

3) What is the measure of the interior angle of a 12-sided figure?

120 degrees

135 degrees

150 degree

160 degrees

To find the measure of the interior angle of a regular polygon, you can use the formula: interior angle = (n-2) * 180 / n, where n is the number of sides. In this case, for a 12-sided figure, the interior angle would be (12-2) * 180 / 12 = 150 degrees.

Explanation

To find the measure of the interior angle of a regular polygon, you can use the formula: interior angle = (n-2) * 180 / n, where n is the number of sides. In this case, for a 12-sided figure, the interior angle would be (12-2) * 180 / 12 = 150 degrees.

4) In a parallelogram, which statement is true regarding the opposite side and opposite angles?

The opposite side and opposite angles of a parallelogram are perpendicular.

The opposite side and opposite angles of a parallelogram are always congruent.

The opposite side and opposite angles of a parallelogram are parallel.

Cosider triangle ABC and CDA

In a parallelogram, the opposite sides are equal in length and the opposite angles are also equal in measure. This is a fundamental property of parallelograms that can be proven by considering the triangles formed within the parallelogram.

Explanation

In a parallelogram, the opposite sides are equal in length and the opposite angles are also equal in measure. This is a fundamental property of parallelograms that can be proven by considering the triangles formed within the parallelogram.