Mathematics · 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

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 sides

  2. Opposite sides

  3. All 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 adjacent sides.

Multiple choice

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

  1. Acute angle

  2. Right angle

  3. Obtuse angle
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In a triangle, the angle opposite the longest side is called the obtuse angle.

Multiple choice

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

  1. Longest side

  2. Shortest side

  3. Middle side
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a triangle, the side opposite the largest angle is called the longest side.

Multiple choice

The exterior angle of a triangle is equal to the sum of the:

  1. Opposite interior angles

  2. Adjacent interior angles

  3. Remote interior angles
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The exterior angle of a triangle is equal to the sum of the remote interior angles.

Multiple choice

In a right triangle, the ratio of the opposite side to the hypotenuse is called the:

  1. Sine

  2. Cosine

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

In a right triangle, the ratio of the opposite side to the hypotenuse is called the sine.

Multiple choice

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

  1. 180 degrees

  2. 270 degrees

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

The sum of the exterior angles of a triangle is always 360 degrees.

Multiple choice

In a triangle, the ratio of the adjacent side to the hypotenuse is called the:

  1. Sine

  2. Cosine

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

In a right triangle, the ratio of the adjacent side to the hypotenuse is called the cosine.

Multiple choice

The ratio of the opposite side to the adjacent side in a right triangle is called the:

  1. Sine

  2. Cosine

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

In a right triangle, the ratio of the opposite side to the adjacent side is called the tangent.

Multiple choice

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

  1. Longest side

  2. Shortest side

  3. Middle side
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a triangle, the side opposite the smallest angle is called the shortest side.

Multiple choice

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

  1. Acute angle

  2. Right angle

  3. Obtuse angle
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In a triangle, the angle opposite the longest side is called the obtuse angle.

Multiple choice

What is the value of the secant of 60 degrees according to Aryabhata?

  1. 0.5

  2. 0.866

  3. 1

  4. 2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Aryabhata calculated the secant of 60 degrees to be 2, which is an accurate approximation.

Multiple choice

What is the sum of the interior angles of a triangle?

  1. 180°

  2. 270°

  3. 360°

  4. 540°
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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. Triangle Inequality Theorem

  3. Angle Sum Theorem

  4. Cosine Rule
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The Angle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees, regardless of the size or shape of the triangle.

Multiple choice

What is the name of the 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. Pythagorean Theorem

  2. Triangle Inequality Theorem

  3. Angle Sum Theorem

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

The Pythagorean Theorem is a fundamental theorem in geometry that relates the side lengths of a right triangle.

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

  3. Law of Cosines

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

The Triangle Sum Theorem, also known as the Angle Sum Property, states that the sum of the interior angles of a triangle is always 180 degrees.