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 angle opposite the hypotenuse is 30 degrees and the adjacent side is 10 cm, what is the length of the opposite side?

  1. 5 cm

  2. 10 cm

  3. 15 cm

  4. 20 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a 30-60-90 triangle, the ratio of the opposite side to the hypotenuse is 1:2. Therefore, the length of the opposite side is (1/2) * 10 cm = 5 cm.

Multiple choice

What is Brahmagupta's theorem on cyclic quadrilaterals?

  1. The sum of the opposite angles of a cyclic quadrilateral is 180 degrees.

  2. The sum of the interior angles of a cyclic quadrilateral is 360 degrees.

  3. The diagonals of a cyclic quadrilateral bisect each other.

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

Brahmagupta's theorem on cyclic quadrilaterals states that the sum of the opposite angles of a cyclic quadrilateral is 180 degrees, the sum of the interior angles of a cyclic quadrilateral is 360 degrees, and the diagonals of a cyclic quadrilateral bisect each other.

Multiple choice

Which of the following is a branch of mathematics that deals with the study of the relationship between angles and sides in triangles?

  1. Algebra

  2. Geometry

  3. Calculus

  4. Trigonometry

  5. Statistics
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Trigonometry is the branch of mathematics that deals with the study of the relationship between angles and sides in triangles.

Multiple choice

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

  1. Pythagorean theorem

  2. Euler's theorem

  3. Fermat's Last Theorem

  4. Goldbach's conjecture
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Pythagorean theorem is a fundamental theorem of 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. It is named after the Greek mathematician Pythagoras, who is believed to have first discovered it.

Multiple choice

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

  1. Pythagorean theorem

  2. Euler's formula

  3. Triangle inequality theorem

  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 angles of a triangle is always 180 degrees.

Multiple choice

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

  1. Pythagorean theorem

  2. Euler's formula

  3. Triangle inequality theorem

  4. Angle addition postulate
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 sides of a right triangle is equal to the square of the hypotenuse.

Multiple choice

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

  1. Pythagorean Theorem

  2. Euler's Theorem

  3. Fermat's Last Theorem

  4. Goldbach's Conjecture
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Pythagorean Theorem, also known as Pythagoras's Theorem, is a fundamental theorem in geometry that establishes the relationship between the sides of a right triangle.

Multiple choice

Two triangles have corresponding sides of 3 cm, 4 cm, and 5 cm, and 6 cm, 8 cm, and 10 cm respectively. Are the triangles similar?

  1. Yes

  2. No
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To determine if the triangles are similar, we need to check if the ratios of their corresponding sides are equal. The ratios are 3/6 = 1/2, 4/8 = 1/2, and 5/10 = 1/2. Since all the ratios are equal, the triangles are similar.

Multiple choice

In a right triangle ABC, the hypotenuse AB is 10 cm and the side AC is 6 cm. If triangle PQR is similar to triangle ABC, where PQ is 15 cm, what is the length of QR?

  1. 9 cm

  2. 12 cm

  3. 15 cm

  4. 18 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since the triangles are similar, the ratio of their corresponding sides is equal. Therefore, AB/PQ = AC/QR. Substituting the given values, we get 10/15 = 6/QR. Solving for QR, we get QR = 12 cm.

Multiple choice

In a right triangle ABC, the hypotenuse AB is 20 cm and the side AC is 12 cm. If triangle PQR is similar to triangle ABC, where PQ is 30 cm, what is the length of QR?

  1. 18 cm

  2. 24 cm

  3. 30 cm

  4. 36 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since the triangles are similar, the ratio of their corresponding sides is equal. Therefore, AB/PQ = AC/QR. Substituting the given values, we get 20/30 = 12/QR. Solving for QR, we get QR = 24 cm.

Multiple choice

In a right triangle ABC, the hypotenuse AB is 30 cm and the side AC is 18 cm. If triangle PQR is similar to triangle ABC, where PQ is 45 cm, what is the length of QR?

  1. 27 cm

  2. 36 cm

  3. 45 cm

  4. 54 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since the triangles are similar, the ratio of their corresponding sides is equal. Therefore, AB/PQ = AC/QR. Substituting the given values, we get 30/45 = 18/QR. Solving for QR, we get QR = 36 cm.

Multiple choice

In a right triangle ABC, the hypotenuse AB is 40 cm and the side AC is 24 cm. If triangle PQR is similar to triangle ABC, where PQ is 60 cm, what is the length of QR?

  1. 36 cm

  2. 48 cm

  3. 60 cm

  4. 72 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since the triangles are similar, the ratio of their corresponding sides is equal. Therefore, AB/PQ = AC/QR. Substituting the given values, we get 40/60 = 24/QR. Solving for QR, we get QR = 48 cm.

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 is one of the most famous theorems in mathematics. It 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 name of the theorem 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?

  1. Pythagorean Theorem

  2. Euler's Theorem

  3. Fermat's Last Theorem

  4. Goldbach's Conjecture
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

Multiple choice

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

  1. 180 degrees

  2. 270 degrees

  3. 360 degrees

  4. 540 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, regardless of the size or shape of the triangle.