## 1. Classify the following triangle. Check all that apply.

A. Equilateral

B. Acute

C. Scalene

D. Isosceles

E. Obtuse

F. Right

**Answer:** D, E.

Isosceles and Obtuse.

### Explanation for Triangle 98^{o}, 41^{o}, 41^{o}

The triangle has two equal sides. Isosceles triangles are triangles with two equal sides. The triangle also has three angles, 98^{o}, 41^{o}, and 41^{o}. Any triangle with angles greater than 90^{o} is an obtuse triangle.

## 2. Classify the following triangle. Check all that apply.

11.9cm, 6cm, 7cm, 132^{o}

A. Scalene

B. Obtuse

C. Isosceles

D. Equilateral

E. Acute

F. Right

**Answer:** A, B.

Scalene and Obtuse

### Explanation for Triangle 11.9cm, 6cm, 7cm, 132^{o}

The triangle has three unequal sides. Scalene triangles are triangles with unequal sides. The triangle has 132^{o} which is greater than 90^{o}. A triangle with an angle greater than 90^{o} is an Obtuse triangle.

## 3. Classify the following triangle. Check all that apply.

A. Equilateral

B. Scalene

C. Right

D. Acute

E. Obtuse

F. Isosceles

**Answer:** C, F.

Right and Isosceles.

### Explanation

Right-angled triangles are referred to as Right Triangles. The triangle has two equal sides. Isosceles triangles are triangles with two equal sides.

## 4. What kind of triangle is the following angles 60^{o}, 60^{o} and 60^{o}?

A. Acute

B. Isosceles

C. Obtuse

D. Right

**Answer:** A

Acute

### Explanation

A Triangle with angles less than 90^{o} is called an Acute Triangle. Based on side classification, a triangle with three equal sides is an Equilateral Triangle.

## Classification of Triangles

Triangles are one of the most common and useful shapes in geometry. They are also some of the most interesting and dynamic shapes, with properties that make them stand out even among other geometric figures. Triangles are usually classified as right or non-right triangles based on their angles. These two types of triangles represent just the tip of the iceberg regarding triangle classification.

There are 7 different types of triangles that share common traits and characteristics. These various types of triangles have unique properties and meanings; each can be used to prove or disprove certain properties regarding other triangles. Let’s explore these 7 types of triangles in greater detail so you can master their properties, relations, and uses.

### Right Triangle

A right triangle is one in which one of the angles is 90° (or one-quarter of a full circle). The hypotenuse is the side opposite the right angle, and the other two sides are the legs. The ratio of the sides of a right triangle is the same for all right triangles, regardless of size. That ratio is the hypotenuse’s square over the leg’s square. The length of the hypotenuse is always greater than or equal to the sum of the leg lengths.

A right triangle is also referred to as an equilateral triangle because it is equi- (meaning “same”) lateral (meaning “two sides”). In a right triangle, one side is exactly the same length as the other side. The third side is the hypotenuse, and it is always the longest side in a right triangle.

### Isosceles Triangle

An isosceles triangle is a right triangle in which two of the sides are the same length, and the third side is longer. The difference between the two sides is that the angles are not both 90 degrees. Isosceles means “same legs.”

Because the angle differences are not equivalent, the hypotenuse of an isosceles triangle is shorter than the two sides of the triangle. If the angle difference is 90 degrees, the triangle is a right triangle.

### Equilateral Triangle

An equilateral triangle has all three sides of the same length. This means that any given angle within the triangle is a multiple of 60 degrees or 1/6th of a full circle.

Because all three sides are the same length, the two shorter sides create the same length as the hypotenuse. Because the triangle is equilateral, the hypotenuse is equal in length to the two shorter sides.

### Acute Triangle

An acute triangle is one in which all three angles are less than 90 degrees. This means that the triangle’s sides are all shorter than the hypotenuse. The smaller the angle, the shorter the sides of the triangle become. In an acute triangle, two sides are shorter than the hypotenuse, while the third side is equal to the hypotenuse.

The ratio of the sides of an acute triangle is the same as a non-right triangle. The difference is that the third side of a non-right triangle is the hypotenuse of the acute triangle.

### Obtuse Triangle

An obtuse triangle is one in which one angle is greater than 90 degrees, and the other two are less. This means that the triangle’s sides are all longer than the hypotenuse. The greater the angle, the longer the sides of the triangle become. In an obtuse triangle, two sides are longer than the hypotenuse, while the third side is shorter than the hypotenuse. The ratio of the sides of an obtuse triangle is the same as a non-right triangle.

The difference is that the third side of a non-right triangle is the shorter side of the obtuse triangle.

### Scalene Triangle

A scalene triangle has no two equal sides and no two equal angles. A scalene triangle is not necessarily an equilateral triangle but rather one without sides or angles of equal length. Because no two sides or angles are the same, the ratio of the sides of a scalene triangle is different for every triangle of that type.

A scalene triangle is also called an irregular triangle because it does not conform to any specific pattern or shape.

### Oblique Triangle

An oblique triangle is a triangle where two sides are of different lengths. Oblique triangles are uncommon in nature and architecture, but they are useful in geometry and related subjects like trigonometry.

## What are the 3 main types of triangles?

Right, isosceles, and equilateral triangles are the three main types of triangles. They are the most common and easy to identify.

## What are the 5 properties of a triangle?

- Shape – The type of triangle and its shape is the first property of a triangle. The three main types are right, isosceles, and equilateral triangles.
- Area – The area of the triangle is the second property of a triangle. The length of each side determines the area of a triangle.
- Height – The height of a triangle is the length of the line drawn from the vertex down to the base.
- Base – The base of a triangle is the length of the line drawn from one vertex down to the other side of the triangle.
- Angle of the triangle –The angle of a triangle is the measurement between two sides of the triangle and the vertex.

## What are the 6 parts of a triangle?

The six parts of a triangle are the three sides and three angles (two vertices and the included angle). The included angle is the angle between the two sides that form the triangle. The two vertices are the beginning and end points of the sides of the triangle. The sides of the triangle are the lines that form the triangle. The third side is the line that goes between the two vertices.

Now that you know more about triangles and their types, let’s explore the three main uses of this geometric shape.

Find Answer to Question: Which conclusion best explain the narrator’s inability to find his own heart in the paragraph on pages 4-5 of the passage?

## Uses of Triangle

### Triangles in Geometry

- Area – The first use of triangles in geometry is the area of the triangle. The area of a triangle is the amount of space taken up by a triangle.
- Types – The second use of triangles in geometry is to identify which type of triangle they are. The three main types of triangles are equilateral, isosceles, and right triangles.
- Angles – The third use of triangles in geometry is to measure the angles of a triangle. You can measure the interior angles of a triangle with a protractor or the triangle theorem.

### Physics

- Center of Gravity – The first use of triangles in physics is to find the center of gravity for an object. The center of gravity is the point where an object would balance if it were to be lifted from any point.
- Triangle Area – The second use of triangles in physics is to find the area of a triangle. The formula to find the area of a triangle is base × height / 2.
- Types – The third use of triangles in physics is to identify which type of triangle they are. The three main types of triangles are equilateral, isosceles, and right triangles.
- Angles – The fourth use of triangles in physics is to measure the angles of a triangle. You can measure the interior angles of a triangle with a protractor or the triangle theorem.

### Triangles in Art

Triangles are symbols of strength and structure and are often used in art. The triangle can be a powerful symbol of balance, harmony, and spirituality, likely contributing to its frequent use in art. Triangles are common in architecture, paintings, fabrics, and clothing. Some of the most iconic examples of the use of triangles in art include the Pyramids of Giza, the Great Seal of the United States, and Leonardo da Vinci’s Vitruvian Man.

Remark

Triangles are classified according to their angles and sides. They also have uses in different fields.