Master right triangle concepts with interactive practice problems. Learn to identify 90-degree angles, calculate missing angles, and solve real-world applications.
A right triangle is a triangle that has one right 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).
Is the triangle in the drawing an acute-angled triangle?
Is the triangle in the drawing a right triangle?
Due to the presence of the 90 degree angle symbol we can determine that this is indeed a right-angled triangle.
Answer:
Yes
In a right triangle, the two sides that form a right angle are called...?
In a right triangle, there are specific terms for the sides. The two sides that form the right angle are referred to as the legs of the triangle. To differentiate, the side opposite the right angle is called the hypotenuse, which is distinct due to being the longest side. Hence, in response to the problem, the sides forming the right angle are correctly identified as Legs.
Answer:
Legs
In a right triangle, the side opposite the right angle is called....?
The problem requires us to identify the side of a right triangle that is opposite to its right angle.
In right triangles, one of the most crucial elements to recognize is the presence of a right angle (90 degrees).
The side that is directly across or opposite the right angle is known as the hypotenuse. It is also the longest side of a right triangle.
Therefore, when asked for the side opposite the right angle in a right triangle, the correct term is the hypotenuse.
Selection from the given choices corroborates our analysis:
Therefore, the correct answer is .
Answer:
Hypotenuse
Fill in the blanks:
In an isosceles triangle, the angle between two ___ is called the "___ angle".
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: 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: .
Answer:
sides, main
In an isosceles triangle, the angle between ? and ? is the "base angle".
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.