Mathematics ยท Quantitative Aptitude

Geometry of Triangles and Angles

846 Questions

Triangle and angle geometry covers angle sums, properties of equilateral shapes, and right triangles. These principles form the basis of advanced quantitative aptitude sections. Practicing spatial problems helps secure points in exams.

Triangle angle sumsPythagorean theoremProperties of equilateral trianglesComplementary and supplementary anglesRight triangle formulas

Geometry of Triangles and Angles Questions

Multiple choice

What is the name of the theorem that states that the sum of the interior angles of a triangle is always 180 degrees?

  1. Pythagorean theorem

  2. Euclid's theorem

  3. Brahmagupta's theorem

  4. Bhaskara's theorem
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Euclid's theorem, also known as the angle sum property of a triangle, states that the sum of the interior angles of a triangle is always 180 degrees.

Multiple choice

What is the Pascal triangle?

  1. A triangular array of numbers where each entry is the sum of the two entries above it.

  2. A triangular array of numbers where each entry is the product of the two entries above it.

  3. A triangular array of numbers where each entry is the difference of the two entries above it.

  4. A triangular array of numbers where each entry is the quotient of the two entries above it.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Pascal triangle is a triangular array of numbers where each entry is the sum of the two entries above it.

Multiple choice

What is the name of the theorem that states that the sum of the angles of a triangle is equal to 180 degrees?

  1. Pythagorean Theorem

  2. Triangle Inequality Theorem

  3. Angle Sum Theorem

  4. Law of Cosines
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The Angle Sum Theorem states that the sum of the angles of a triangle is equal to 180 degrees. This theorem is attributed to Indian mathematicians.

Multiple choice

What is the name of the theorem that states that the volume of a pyramid is equal to one-third the product of its base area and height?

  1. Pythagorean Theorem

  2. Triangle Inequality Theorem

  3. Angle Sum Theorem

  4. Volume of a Pyramid Formula
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The Volume of a Pyramid Formula states that the volume of a pyramid is equal to one-third the product of its base area and height. This formula is attributed to Indian mathematicians.

Multiple choice

What is the name of the mathematical theorem that states that the sum of the interior angles of a triangle is always 180 degrees?

  1. Pythagorean Theorem

  2. Triangle Inequality Theorem

  3. Law of Cosines

  4. Angle Addition Postulate
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The Angle Addition Postulate states that the sum of the interior angles of a triangle is always 180 degrees.

Multiple choice

In a right triangle, the angle opposite the hypotenuse is called the:

  1. Adjacent angle

  2. Opposite angle

  3. Hypotenuse angle

  4. Complementary angle
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a right triangle, the angle opposite the hypotenuse is known as the opposite angle.

Multiple choice

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the:

  1. Adjacent and opposite sides

  2. Opposite and hypotenuse sides

  3. Adjacent and hypotenuse sides

  4. All sides
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Pythagorean theorem relates the squares of the sides of a right triangle.

Multiple choice

The sine of an angle is defined as the ratio of the:

  1. Opposite side to the adjacent side

  2. Opposite side to the hypotenuse

  3. Adjacent side to the hypotenuse

  4. Hypotenuse to the opposite side
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The sine of an angle is calculated by dividing the opposite side by the hypotenuse.

Multiple choice

The cosine of an angle is defined as the ratio of the:

  1. Adjacent side to the hypotenuse

  2. Opposite side to the hypotenuse

  3. Adjacent side to the opposite side

  4. Hypotenuse to the adjacent side
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The cosine of an angle is calculated by dividing the adjacent side by the hypotenuse.

Multiple choice

In a right triangle, the side opposite the right angle is called the:

  1. Hypotenuse

  2. Adjacent side

  3. Opposite side
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The side opposite the right angle in a right triangle is called the opposite side.

Multiple choice

The sum of the interior angles of a triangle is always:

  1. 180 degrees

  2. 270 degrees

  3. 360 degrees
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The sum of the interior angles of a triangle is always 180 degrees.

Multiple choice

The Pythagorean theorem states that in a right triangle, the square of the:

  1. Hypotenuse is equal to the sum of the squares of the other two sides

  2. Opposite side is equal to the sum of the squares of the other two sides

  3. Adjacent side is equal to the sum of the squares of the other two sides
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Multiple choice

The measure of an angle that is greater than 90 degrees and less than 180 degrees is called:

  1. Acute angle

  2. Obtuse angle

  3. Right angle
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The measure of an angle that is greater than 90 degrees and less than 180 degrees is called an obtuse angle.

Multiple choice

What is the name of the Chinese theorem that states that the sum of the interior angles of a triangle is always 180 degrees?

  1. The Pythagorean Theorem

  2. The Triangle Inequality

  3. The Law of Cosines

  4. The Angle Sum Theorem
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The Angle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees. This theorem was first discovered by Chinese mathematicians in the 1st century CE.

Multiple choice

What is the name of the Chinese theorem that states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse?

  1. The Pythagorean Theorem

  2. The Triangle Inequality

  3. The Law of Cosines

  4. Heron's Formula
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Pythagorean Theorem states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse. This theorem was first discovered by Chinese mathematicians in the 6th century BCE.