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, if the hypotenuse and one leg are congruent to the hypotenuse and one leg of another right triangle, then the triangles are:

  1. Congruent

  2. Similar

  3. Isosceles

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

By the Hypotenuse-Leg (HL) congruence theorem, if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Multiple choice

In a triangle, if two sides are congruent and the third side is not congruent, then the triangle is:

  1. Congruent

  2. Similar

  3. Isosceles

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

A triangle with two congruent sides and one non-congruent side is called an isosceles triangle.

Multiple choice

In a triangle, if all three sides are congruent, then the triangle is:

  1. Congruent

  2. Similar

  3. Equilateral

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

A triangle with all three sides congruent is called an equilateral triangle.

Multiple choice

Two triangles are similar if they have:

  1. Congruent sides and angles

  2. Similar sides and angles

  3. Equal areas

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Two triangles are similar if they have similar sides and angles, but not necessarily congruent sides and angles.

Multiple choice

If two triangles are similar, then their corresponding:

  1. Sides are proportional

  2. Angles are congruent

  3. Areas are proportional

  4. All of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If two triangles are similar, then their corresponding sides are proportional, their corresponding angles are congruent, and their corresponding areas are proportional.

Multiple choice

In a right triangle, if the hypotenuse is congruent to the hypotenuse of another right triangle, then the triangles are:

  1. Congruent

  2. Similar

  3. Isosceles

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

By the Hypotenuse-Hypotenuse (HH) similarity theorem, if the hypotenuse of one right triangle is congruent to the hypotenuse of another right triangle, then the triangles are similar.

Multiple choice

In a triangle, if two angles are congruent and the third angle is not congruent, then the triangle is:

  1. Congruent

  2. Similar

  3. Isosceles

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

A triangle with two congruent angles and one non-congruent angle is called an isosceles triangle.

Multiple choice

In a triangle, if one angle is 90 degrees, then the triangle is:

  1. Congruent

  2. Similar

  3. Right

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

A triangle with one angle measuring 90 degrees is called a right triangle.

Multiple choice

In a triangle, if the sum of the squares of two sides is equal to the square of the third side, then the triangle is:

  1. Congruent

  2. Similar

  3. Right

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

By the Pythagorean theorem, in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse).

Multiple choice

In a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then the triangle is:

  1. Congruent

  2. Similar

  3. Right

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

By the converse of the Pythagorean theorem, 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

What is the Pythagorean theorem?

  1. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

  2. In a right triangle, the square of the hypotenuse is equal to the difference of the squares of the other two sides.

  3. In a right triangle, the square of the hypotenuse is equal to the product of the squares of the other two sides.

  4. In a right triangle, the square of the hypotenuse is equal to the quotient 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

What is the angle between two orthogonal vectors?

  1. 0 degrees

  2. 90 degrees

  3. 180 degrees

  4. 270 degrees
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The angle between two orthogonal vectors is 90 degrees.

Multiple choice

What is the name of the theorem that establishes a relationship between the sides and angles of a right triangle?

  1. Pythagoras' Theorem

  2. Euler's Formula

  3. Fermat's Last Theorem

  4. Gauss's Theorem
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Pythagoras' Theorem, also known as the Pythagorean Theorem, is a fundamental theorem in geometry that relates the sides and angles of a right triangle. It states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Multiple choice

What is the name of the famous theorem that relates the sum of the interior angles of a triangle to 180 degrees?

  1. Euler's Formula

  2. Gauss's Theorem

  3. Pythagoras' Theorem

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

The Triangle Sum Theorem, also known as the Angle Sum Theorem, is a fundamental theorem in geometry that states that the sum of the interior angles of a triangle is always equal to 180 degrees.

Multiple choice

Which theorem 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 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 is a fundamental property of triangles and is used in many areas of mathematics and geometry.