# Isosceles Triangle – Definition, Angles, Properties, Examples

Confused about isosceles triangles? Don’t worry! This guide will show you all you need to know. We’ll explain the meaning, angles, features, and provide examples. Get ready to discover the awesomeness of isosceles triangles!

## Introduction to Isosceles Triangle

An isosceles triangle has two sides of equal length and two equal angles opposite those sides. The third side is the base, and it’s either longer or shorter.

These triangles have special properties:

• The angles opposite the equal sides are the same.
• The angle between the two equal sides divides the vertex angle.
• The altitude makes two congruent right triangles by bisecting the base.

You can see isosceles triangles in everyday things like rooflines of houses, guitar picks, and geometry problems. They help us find missing angles and side lengths.

## Definition of Isosceles Triangle

An isosceles triangle is a shape with two equal sides and two equal angles.

Properties:

• Opposite sides have equal measure.
• The base angles, opposite to the equal sides, have same measure.
• A median drawn from the vertex angle divides the triangle into two congruent right triangles.

Examples:

• Equilateral triangles have three sides and angles of same measure (60 degrees).
• Triangles with two sides of equal length and a third side of different length (e.g. 5 cm, 5 cm, 7 cm).

## Angles of Isosceles Triangle

An isosceles triangle has two equal sides and angles. The angles are based on the ratio between the length of the base and the sides. Let b be the length of the base and s be the length of the sides.

To work out the angle opposite the base, use this formula: A = 180 – (2 x arctan(b/(2s))).

The angles opposite the sides are equal and can be found by using B = C = (180 – A)/2.

For instance, if the base is 6cm and the sides are 5cm, A = 72.34 degrees. Therefore, the angles opposite the sides are 53.83 degrees each.

Fun Fact: The Great Pyramids of Giza are isosceles triangles, as every side is an isosceles triangle with the same measurements.

## Properties of Isosceles Triangle

An isosceles triangle is a shape with two sides of the same length. Opposite these sides are two equal angles. The third side, which is unequal, is opposite to a unique angle.

Here are some properties of an isosceles triangle to consider:

• Two congruent sides and angles.
• A vertex angle and two base angles.
• The base angles are always congruent.
• The angle bisector divides the vertex angle and the opposite side.
• The median from the vertex angle splits the base into two equal parts.

Examples of isosceles triangles include airplane wings and some roof shapes.

## Types of Isosceles Triangle

An isosceles triangle has three sides of equal length. But two of those sides are parallel. These triangles have three types. Each type has particular angles and properties.

• The acute isosceles triangle has all angles less than 90 degrees. The two base angles are the same. The vertex angle is greater than both.
• In a right isosceles triangle, one angle is exactly 90 degrees. The other two angles are equal. These are the base angles.
• An obtuse isosceles triangle has one angle greater than 90 degrees. The other two angles are equal. The obtuse angle is the vertex angle.

We can find isosceles triangles in various structures and shapes. Like a roof of a house, a flag banner and certain geometric proofs.

## Applications of Isosceles Triangle

An isosceles triangle has two equal sides and two equal angles. It’s a fundamental shape in geometry. It has many uses.

Here are some of its uses:

1. Architectural Design: It’s used to design arches, doorways, windows and trusses.
2. Pyramids: The Great Pyramid of Giza is an isosceles triangle based structure.
3. Navigation: In navigation, two bearings form an isosceles triangle with the vessel at the apex.
4. Maths and Science: Isosceles triangles are used in maths problems, proofs, and formulas.
5. Sports: Soccer goals and basketball backboards use isosceles triangles.

Isosceles triangles can help with study and daily tasks.

## Examples of Isosceles Triangle

An isosceles triangle is a polygon with two equal sides and two equal angles. Here are three classic examples:

1. A triangle with two sides of 5 cm and one side of 6 cm. This is an isosceles triangle because the two shorter sides are equal in length.
2. A triangle with two angles of 70 degrees and one of 40 degrees. This is an isosceles triangle because the two equal angles are each 70 degrees.
3. A triangle with one angle of 120 degrees and two of 30 degrees. This is an isosceles triangle because the two equal angles are each 30 degrees.

## Conclusion

In the end, an isosceles triangle is a polygon with two sides and angles that are equal. Its features include:

• The angles across from the same sides are the same.
• The base angles (the angles next to the base) are the same.
• The median, height, and angle bisector drawn from the vertex of the two same sides are the same line.

Examples of isosceles triangles:

• 5cm, 5cm, 6cm
• 8in, 8in, 10in.

Knowing the properties of isosceles triangles can help solve math problems and make geometric constructions.

### 1. What is an isosceles triangle?

An isosceles triangle is a triangle with two sides of equal length and two equal angles.

### 2. What is the definition of an isosceles triangle?

An isosceles triangle is defined as a triangle with two sides of equal length and two equal angles opposite those sides.

### 3. What are the properties of an isosceles triangle?

The properties of an isosceles triangle include having two sides of equal length and two equal angles opposite those sides. The angle between the two equal sides is known as the vertex angle.

### 4. What is the formula for finding the area of an isosceles triangle?

The formula for finding the area of an isosceles triangle is A = (1/2)bh, where b is the length of the base and h is the height of the triangle.

### 5. What are some examples of isosceles triangles?

Examples of isosceles triangles include triangles with two sides of equal length and two equal angles, such as an equilateral triangle.

### 6. How do you find the measure of the angles in an isosceles triangle?

In an isosceles triangle, the measure of the vertex angle can be found by subtracting the sum of the other two angles from 180 degrees and dividing the result by 2.

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