The isosceles triangle is a type of triangle that has two sides (legs) of equal length.
A consequence of having two sides of equal length implies that also the two angles opposite these sides measure the same.
Isosceles triangle
Test yourself on types of triangles!
In a right triangle, the side opposite the right angle is called....?
In an isosceles triangle the two equal sides are called legs and the third is called the base and in most exercises acts as the base.
The angle that lies between the two equal sides is called the angle at the vertex (or apex angle).
The two angles adjacent to the base are called base angles and measure the same.
Furthermore, the base angles that measure the same cannot be obtuse (more than ) or right angles (equal to ), because their measures would add up to at least 180°, therefore, they have to be acute (less than ).
The above causes the isosceles triangle to be further classified as obtuse, right or acute, depending on how the vertex angle is.
Next, we will see some examples of isosceles triangles:
Isosceles triangle
Examples of isosceles triangles
We will demonstrate the characteristics of isosceles triangles by means of an exercise.
Given the isosceles triangle as shown in the figure.
Use the data shown in the illustration to calculate the angles L and M.
We will start with the triangle . We already know two angles, so we can calculate the third angle (The sum of the interior angles of a triangle is degrees). Thus, the angle measures degrees (since ).
Since we know that the triangle is isosceles we understand that its base angles and are equal.
Therefore
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 ?
Question 2
In a right triangle, the two sides that form a right angle are called...?
Question 3
Is the triangle in the drawing a right triangle?
Questions on the subject
What is an isosceles triangle?
It is a triangle that has two sides of equal length.
What is an acute isosceles triangle?
It is an isosceles triangle whose angle at the vertex measures less than.
What is a right isosceles triangle?
It is an isosceles triangle whose angle at the vertex measures exactly .
If you are interested in learning more about other triangle topics, you can enter one of the following articles:
- Acute triangle
- Obtuse triangle
- Scalene Triangle
- Equilateral triangle
- The edges of a triangle
- Area of a right triangle
- Height of a triangle
- How to calculate the area of a triangle
- How to calculate the perimeter of a triangle?
- Addition and difference of angles
On the Tutorela blog you will find a variety of articles about mathematics.
Ejemplos y ejercicios con soluciones de triángulo isósceles
Exercise #1
What kind of triangle is given in the drawing?
Video Solution
Step-by-Step Solution
As all the angles of a triangle are less than 90° and the sum of the angles of a triangle equals 180°:
The triangle is isosceles.
Answer
Isosceles triangle
Exercise #2
Given the values of the sides of a triangle, is it a triangle with different sides?
Video Solution
Step-by-Step Solution
As is known, a scalene triangle is a triangle in which each side has a different length.
According to the given information, this is indeed a triangle where each side has a different length.
Answer
Yes
Exercise #3
Which kind of triangle is given in the drawing?
Video Solution
Step-by-Step Solution
As we know that sides AB, BC, and CA are all equal to 6,
All are equal to each other and, therefore, the triangle is equilateral.
Answer
Equilateral triangle
Exercise #4
Is the triangle in the drawing a right triangle?
Step-by-Step Solution
Due to the presence of the 90 degree angle symbol we can determine that this is indeed a right-angled triangle.
Answer
Yes
Exercise #5
What kid of triangle is the following
Video Solution
Step-by-Step Solution
Given that in an obtuse triangle it is enough for one of the angles to be greater than 90°, and in the given triangle we have an angle C greater than 90°,
Furthermore, the sum of the angles of the given triangle is 180 degrees so it is indeed a triangle:
The triangle is obtuse.
Answer
Obtuse Triangle
Do you know what the answer is?
Question 1
Is the triangle in the drawing a right triangle?
Question 2
Fill in the blanks:
In an isosceles triangle, the angle between two ___ is called the "___ angle".
Question 3
Is the triangle in the drawing a right triangle?
More Questions
Types of Triangles
- Right Triangle Area Problem: Solve for X When Area = 6 cm²
- Triangle Classification: Identifying a Right Triangle with 90-Degree Angle
- Triangle Classification: Identifying a Shape with 70°, 70°, and 40° Angles
- Triangle Classification: Determine Type with Angles 39°, 107°, and 34°
- Square Diagonal Properties: Classifying Triangles ABC and ACD
Related Subjects
- Area
- Trapezoids
- Area of a trapezoid
- Perimeter of a trapezoid
- Parallelogram
- The area of a parallelogram: what is it and how is it calculated?
- Perimeter of a Parallelogram
- Kite
- Area of a Deltoid (Kite)
- Congruent Triangles
- Angles In Parallel Lines
- Alternate angles
- Corresponding angles
- Collateral angles
- Vertically Opposite Angles
- Adjacent angles
- The Pythagorean Theorem
- Elements of the circumference
- Circle
- Diameter
- Pi
- Area of a circle
- The Circumference of a Circle
- The Center of a Circle
- Radius
- How is the radius calculated using its circumference?
- Rectangle
- Calculating the Area of a Rectangle
- The perimeter of the rectangle
- Congruent Rectangles
- The sides or edges of a triangle
- Similarity of Triangles and Polygons
- Triangle similarity criteria
- Triangle Height
- Midsegment
- Midsegment of a triangle
- The Sum of the Interior Angles of a Triangle
- Exterior angles of a triangle
- Relationships Between Angles and Sides of the Triangle
- Relations Between The Sides of a Triangle
- Rhombus, kite, or diamond?
- The Area of a Rhombus
- Perimeter
- Triangle
- The Area of a Triangle
- Area of a right triangle
- Area of Isosceles Triangles
- Area of a Scalene Triangle
- Area of Equilateral Triangles
- Perimeter of a triangle
- Right Triangular Prism
- Bases of the Right Triangular Prism
- The lateral faces of the prism
- Lateral Edges of a Prism
- Height of a Prism
- The volume of the prism
- Surface area of triangular prisms
- Areas of Polygons for 7th Grade
- Area of a right-angled trapezoid
- Area of an isosceles trapezoid
- Corresponding exterior angles
- Alternate interior angles
- Height in a triangle
- Center of a Triangle - The Centroid - The Intersection Point of Medians
- How do we calculate the area of complex shapes?
- How to calculate the area of a triangle using trigonometry?
- How do we calculate the perimeter of polygons?
- All terms in triangle calculation
- Parts of a Circle
