A right triangle is a triangle that has oneright angle, meaning an angle of 90 degrees. Based on the fact that the sum of angles in any triangle is 180 degrees, we can conclude that the sum of the two remaining angles in a right triangle is 90 degrees. This means that both angles must be acute (less than 90 degrees).
In a right triangle, the side opposite the right angle is called....?
Incorrect
Correct Answer:
Hypotenuse
Practice more now
Here are some examples of right triangles:
Exercise
For example, let's take any right triangle. It is known that one of the angles in this triangle is 45 degrees. We are asked to find the second acute angle in the given triangle.
Since this is a right triangle, meaning one of the angles equals 90 degrees, we can calculate and find that the second acute angle will be equal to 45 degrees. Why? Because it complements the first given acute angle to 90 degrees.
Join Over 30,000 Students Excelling in Math!
Endless Practice, Expert Guidance - Elevate Your Math Skills Today
Test your knowledge
Question 1
In an isosceles triangle, what are each of the two equal sides called ?
Incorrect
Correct Answer:
Legs
Question 2
In a right triangle, the two sides that form a right angle are called...?
Incorrect
Correct Answer:
Legs
Question 3
Is the triangle in the drawing a right triangle?
Incorrect
Correct Answer:
Yes
Examples with solutions for Types of Triangles
Exercise #1
In an isosceles triangle, the angle between ? and ? is the "base angle".
Step-by-Step Solution
An isosceles triangle is one that has at least two sides of equal length. The angles opposite these two sides are known as the "base angles."
The side that is not equal to the other two is referred to as the "base" of the triangle. Thus, the "base angles" are the angles between each of the sides that are equal in length and the base.
Therefore, when we specify the angle in terms of its location or position, it is the angle between a "side" and the "base." This leads to the conclusion that the angle between the side and the base is the "base angle."
Therefore, the correct choice is Side, base.
Answer
Side, base.
Exercise #2
In an isosceles triangle, what are each of the two equal sides called ?
Step-by-Step Solution
In an isosceles triangle, there are three sides: two sides of equal length and one distinct side. Our task is to identify what the equal sides are called.
To address this, let's review the basic properties of an isosceles triangle:
An isosceles triangle is defined as a triangle with at least two sides of equal length.
The side that is different in length from the other two is usually called the "base" of the triangle.
The two equal sides of an isosceles triangle are referred to as the "legs."
Therefore, each of the two equal sides in an isosceles triangle is called a "leg."
In our problem, we confirm that the correct terminology for these two equal sides is indeed "legs," distinguishing them from the "base," which is the unequal side. This aligns with both the typical definitions and properties of an isosceles triangle.
Thus, the equal sides in an isosceles triangle are known as legs.
Answer
Legs
Exercise #3
In an isosceles triangle, the third side is called?
Step-by-Step Solution
To solve this problem, we need to understand what an isosceles triangle is and how its sides are labeled:
In an isosceles triangle, there are two sides that have equal lengths. These are typically called the "legs" of the triangle.
The third side, which is not necessarily of equal length to the other two sides, is known as the "base."
In terms of the problem, we want to determine the term used for the third side, which is the side that is not one of the two equal sides.
The correct term for the third side in an isosceles triangle is the "base." This is because the third side serves as a different function compared to the equal sides, which usually form the symmetrical parts of the triangle.
Among the given answer choices, choosing "Base" correctly identifies the third side of an isosceles triangle.
Therefore, the third side in an isosceles triangle is called the base.
Final Solution: Base
Answer
Base
Exercise #4
Fill in the blanks:
In an isosceles triangle, the angle between two ___ is called the "___ angle".
Step-by-Step Solution
In order to solve this problem, we need to understand the basic properties of an isosceles triangle.
An isosceles triangle has two sides that are equal in length, often referred to as the "legs" of the triangle. The angle formed between these two equal sides, which are sometimes referred to as the "sides", is called the "vertex angle" or sometimes more colloquially as the "main angle".
When considering the vocabulary of the given multiple-choice answers, choice 2: sides,main accurately fills the blanks, as the angle formed between the two equal sides can indeed be referred to as the "main angle".
Therefore, the correct answer to the problem is: sides,main.
Answer
sides, main
Exercise #5
Is the triangle in the drawing a right triangle?
Step-by-Step Solution
To determine if the given triangle is a right triangle, we will analyze its geometrical properties. In a right triangle, one of its angles must be 90∘. The easiest method to identify a right triangle without specific numerical coordinates is to check if any of the angles form a right angle just by visual assessment or conceptual understanding; this method can use the Pythagorean theorem in reverse if sides are measure-known.
In this setting, instead of physical measurements or accessible labeled SVG points, only the geometrical visual approach is taken. If based on generalized drawing inspections, assuming there is no visually postulated straight 90-degree form visible without a numerical validation, it's assumed to not initially exhibit such requirements when no arithmetic sides are comparatively used.
The lack of specific side lengths that conform to the Pythagorean theorem implies that, without other noticed forms or vectors increment constructs delivering a forced angle view, the triangle doesn't conform to being considered right.
Therefore, the triangle in the drawing is not a right triangle based on this lack of definitional evidence when view or vertex distinctions are ensured.