Types Of Triangles Quiz Questions

A triangle with no congruent sides is called a scalene triangle. Additionally, a triangle with one angle greater than 90 degrees is known as an obtuse triangle. Therefore, a triangle that has no congruent sides and one angle greater than 90 degrees is classified as an obtuse scalene triangle. This type of triangle has all sides of different lengths (scalene) and one angle that is greater than 90 degrees (obtuse).

A triangle with one 90 degree angle is called a right triangle. In a right triangle, one of the angles measures exactly 90 degrees, making it the largest angle in the triangle. The other two angles in a right triangle are acute angles, meaning they are less than 90 degrees. Therefore, the correct answer is right.

An acute triangle is a triangle where all three angles measure less than 90 degrees. This means that none of the angles in the triangle are right angles (90 degrees) or obtuse angles (greater than 90 degrees).

The correct answer is 180 degrees because the sum of the interior angles of any triangle is always equal to 180 degrees. This is a fundamental property of triangles in Euclidean geometry. No matter the size or shape of the triangle, the sum of its three interior angles will always be 180 degrees.

An equilateral triangle is a triangle where all sides are congruent. This means that all three sides of the triangle have the same length. In contrast, a scalene triangle has no congruent sides, and an isosceles triangle has two congruent sides. Therefore, the correct answer is equilateral.

An isosceles triangle is characterized by having two sides of equal length, which are called the legs. The angles opposite these equal sides are also equal. This symmetry gives the isosceles triangle its distinctive properties, such as equal altitudes and medians from the equal angles. Isosceles triangles are commonly used in architecture and design because of their symmetrical properties.

In a right triangle, the side opposite the right angle (90 degrees) is known as the hypotenuse. This is the longest side of the triangle because, according to the Pythagorean theorem, the square of the hypotenuse’s length is equal to the sum of the squares of the other two sides. This theorem is a fundamental principle in trigonometry and is used extensively in various fields of science and engineering.

To find angle C, use the Law of Cosines:

c^2=a^2+b^2−2ab⋅cos⁡C

Substituting a=13, b=14 cm, and c=15 cm:

15^2=13^2+14^2−2×13×14×cos⁡C

225=169+196−364×cos⁡C

225=365−364×cos⁡C

Cos⁡C=140/364=0.3846

Thus, C≈cos⁡−1(0.3846)≈75.5°C

To check if the triangle is right-angled, use the Pythagorean theorem:

7^2+24^2=49+576=625=25^2

Since the sides satisfy the Pythagorean theorem, the triangle is right-angled.