Geometry Test 1

A straight angle is 180°.

• True

• False

Answer explanation

A straight angle is defined as an angle that measures exactly 180°. Therefore, the statement is true.

An obtuse triangle may have only one obtuse angle.

• True

• False

Answer explanation

True. An obtuse triangle can only have one obtuse angle because the sum of all angles in a triangle is 180 degrees. If there were two obtuse angles, their sum would exceed 180 degrees, which is not possible.

Two quantities equal to the same quantity are equal to each other.

• True

• False

Answer explanation

This statement is true because of the transitive property of equality. If two quantities are both equal to a third quantity, they must be equal to each other.

If two lines are perpendicular, do they form right angles?

• True

• False

Answer explanation

True. When two lines are perpendicular, they intersect at a 90-degree angle, which is defined as a right angle. Therefore, perpendicular lines always form right angles.

If a triangle is equilateral, it is also acute.

• True

• False

Answer explanation

An equilateral triangle has all angles equal to 60 degrees, which are all less than 90 degrees. Therefore, it is classified as an acute triangle. Thus, the statement is true.

If two angles are equal, are they supplementary?

• True

• False

Answer explanation

Two angles are equal if they have the same measure. Supplementary angles, however, must add up to 180 degrees. Therefore, equal angles can be supplementary only if they each measure 90 degrees, making the statement generally false.

A bisector of one angle of a triangle is perpendicular to the opposite side.

• True

• False

Answer explanation

The statement is false because a bisector of an angle in a triangle is not necessarily perpendicular to the opposite side. It only divides the angle into two equal parts, without any requirement for perpendicularity.

A right triangle may also be obtuse.

• True

• False

Answer explanation

A right triangle cannot be obtuse because it has one angle that is exactly 90 degrees. An obtuse triangle has one angle greater than 90 degrees, which contradicts the definition of a right triangle. Therefore, the statement is false.

Two angles whose sum is a right angle are said to be supplementary.

• True

• False

Answer explanation

The statement is false. Two angles whose sum is a right angle are called complementary, not supplementary. Supplementary angles sum to 180 degrees.

The legs of an isosceles triangle are equal.

• True

• False

Answer explanation

In an isosceles triangle, by definition, two sides (the legs) are of equal length. Therefore, the statement that the legs of an isosceles triangle are equal is True.