Always Sometimes Never

Front

The Triangles are Congruent if two sides and an angles of one are congruent to the corresponding parts of the other

Back

Sometimes

Answer explanation

Triangles are sometimes congruent if two sides and an angle of one triangle are congruent to the corresponding parts of another. This is known as the Side-Angle-Side (SAS) criterion, but it does not apply in all cases.

Front

If two sides of a right triangle are congruent to the corresponding parts of another right triangle, are the triangles congruent?

Back

Always

Answer explanation

The statement is true because if two sides of one right triangle are congruent to two sides of another right triangle, the triangles must be congruent by the Hypotenuse-Leg theorem. Therefore, the correct answer is 'Always'.

Front

All three altitudes of a triangle fall outside the triangle.

Back

Never

Answer explanation

In a triangle, at least one altitude always lies inside the triangle. Therefore, it is impossible for all three altitudes to fall outside the triangle. Thus, the correct answer is 'Never'.

Front

A right triangle is congruent to an obtuse triangle

Back

Never

Answer explanation

A right triangle has one 90-degree angle, while an obtuse triangle has one angle greater than 90 degrees. Since their angle measures differ fundamentally, a right triangle can never be congruent to an obtuse triangle.

Front

If a triangle is obtuse, it is isosceles

Back

Sometimes

Answer explanation

An obtuse triangle can be isosceles (two equal sides) or scalene (all sides different). Therefore, it is not always isosceles, making 'Sometimes' the correct choice.

Front

The bisector of the vertex angle of a scalene triangle is perpendicular to the base?

Back

Never

Answer explanation

In a scalene triangle, the angle bisector of the vertex angle does not necessarily bisect the base at a right angle. Therefore, it is never true that the bisector is perpendicular to the base.

Front

The acute angles of a right triangle are complementary.

Back

Always

Answer explanation

In a right triangle, the sum of the angles is always 180 degrees. One angle is 90 degrees, leaving 90 degrees for the two acute angles. Since they add up to 90 degrees, they are complementary. Thus, the acute angles are always complementary.

Front

The supplement of one of the angles of a triangle is equal in measure to the sum of the other two angles of the triangle.

Back

Always

Answer explanation

In a triangle, the sum of the angles is always 180 degrees. The supplement of one angle (180 - angle) equals the sum of the other two angles, which is always true. Therefore, the statement is always correct.

Front

A Triangle contains two obtuse angles

Back

Never

Answer explanation

A triangle cannot have two obtuse angles because the sum of all angles in a triangle is 180 degrees. If two angles are obtuse (greater than 90 degrees), their sum would exceed 180 degrees, making it impossible.

Front

A Triangle is a plane figure

Back

Always

Answer explanation

A triangle is defined as a plane figure with three sides and three angles. Therefore, it is correct to say that a triangle is always a plane figure.