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

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This statement is known as the:

  1. Pythagorean Theorem

  2. Euclidean Theorem

  3. Converse of Pythagorean Theorem

  4. Leg Theorem
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Pythagorean Theorem is a fundamental theorem in geometry that 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

If the legs of a right triangle are 3 cm and 4 cm, what is the length of the hypotenuse?

  1. 5 cm

  2. 7 cm

  3. 12 cm

  4. 16 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the Pythagorean Theorem, we have: (a^2 + b^2 = c^2). Substituting the values, we get: (3^2 + 4^2 = c^2). Simplifying, we get: (9 + 16 = c^2). Therefore, (c^2 = 25) and (c = 5).

Multiple choice

In a right triangle, if the hypotenuse is 10 cm and one leg is 6 cm, what is the length of the other leg?

  1. 4 cm

  2. 8 cm

  3. 12 cm

  4. 16 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the Pythagorean Theorem, we have: (a^2 + b^2 = c^2). Substituting the values, we get: (6^2 + b^2 = 10^2). Simplifying, we get: (36 + b^2 = 100). Therefore, (b^2 = 64) and (b = 8).

Multiple choice

In a right triangle, the ratio of the square of the hypotenuse to the square of one leg is equal to the ratio of the square of the other leg to the square of the hypotenuse. This statement is known as the:

  1. Converse of Pythagorean Theorem

  2. Leg Theorem

  3. Pythagorean Triple

  4. Pythagorean Identity
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Converse of Pythagorean Theorem states that if the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

Multiple choice

In a right triangle, the square of the hypotenuse is equal to the difference of the squares of the other two sides. True or False?

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, not the difference.

Multiple choice

What is the center of mass of a triangle?

  1. The center of the triangle

  2. The midpoint of a side of the triangle

  3. The intersection of the medians of the triangle

  4. The vertex of the triangle
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The center of mass of a triangle is the intersection of the medians of the triangle. This is because the mass of the triangle is evenly distributed throughout its area.