Test your knowledge on the properties, types, and theorems of triangles! By, Sebastian Castañeda
1
What is the sum of the interior angles of any triangle?
2
In an equilateral triangle, what is the measure of each angle?
3
According to the Pythagorean theorem, what is the formula for a right triangle?
4
Which triangle has all sides of different lengths?
5
What is the area of a triangle with a base of 6 cm and a height of 4 cm?
6
In a right triangle, the two shorter sides form the right angle. What is the name of the longest side, which is opposite the right angle?
7
A triangle has two sides of equal length and one side that is different in length. What is the name of this type of triangle?
8
In any triangle, the exterior angles are formed by extending the sides of the triangle. What is the total sum of these exterior angles?
9
If the sum of two sides of a triangle is always greater than the third side, which set of side lengths can form a triangle?
10
Given a triangle with sides of lengths 5 cm, 5 cm, and 6 cm, what can you infer about the type of triangle, and what is the height if a perpendicular is drawn from the vertex opposite the unequal side?
Explicación
The sum of the interior angles of any triangle is always 180°. This is true for all types of triangles, including equilateral, isosceles, and scalene triangles.
In an equilateral triangle, all sides are equal. Because of this, all three angles are also equal, and each angle measures 60°
In a right triangle, the sum of the square of the two shorter sides (a and b) is equal to the square of the longest side (c), which is called the hypotenuse.
The formula for the area of a triangle is: Area = (base × height) ÷ 2. For this triangle, Area = (6 × 4) ÷ 2 = 12 cm²
in any right triangle, the two shorter sides meet to form the right angle. The side opposite the right angle is called the hypotenuse, and it is always the longest side.
An isosceles triangle is a type of triangle where two sides are the same length, and the third side is a different length. This is different from an equilateral triangle, where all three sides are the same, and a scalene triangle, where all three sides are different.
The exterior angles of a triangle are formed when you extend its sides. The sum of these exterior angles, for any triangle, is always 360°, no matter the type of triangle.
For any set of three lengths to form a triangle, the sum of any two sides must be greater than the third side. In this case, 6 + 9 > 15, 9 + 15 > 6, and 6 + 15 > 9, so these lengths can form a triangle.
This is an isosceles triangle because two of its sides are equal (5 cm and 5 cm). The height can be calculated by drawing a perpendicular from the opposite vertex to the unequal side (6 cm). Using the Pythagorean theorem, we find that the height is 4 cm.
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