Types of Triangles Practice Problems and Worksheets

Master triangle classification with interactive practice problems. Learn equilateral, isosceles, scalene, right, acute, and obtuse triangles through step-by-step solutions.

📚What You'll Master in Triangle Types Practice
  • Identify and classify triangles by side lengths: equilateral, isosceles, and scalene
  • Distinguish between acute, right, and obtuse triangles using angle measurements
  • Apply the Pythagorean theorem to solve right triangle problems
  • Calculate missing angles using the 180-degree angle sum property
  • Determine triangle areas using base and height formulas
  • Solve real-world problems involving triangle properties and measurements

Understanding Types of Triangles

Complete explanation with examples

Properties of triangles

The triangle is a geometric figure with three sides that form three angles whose sum is always 180o 180^o degrees.

A - Properties of triangles

Its vertices are called A,B A,B and C C

The union between these vertices creates the edges AB,BC AB,BC and CA CA
There are several types of triangles that we will study in this article.

Detailed explanation

Practice Types of Triangles

Test your knowledge with 20 quizzes

Given the values of the sides of a triangle, is it a triangle with different sides?

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Examples with solutions for Types of Triangles

Step-by-step solutions included
Exercise #1

Is the triangle in the drawing an acute-angled triangle?

Step-by-Step Solution

An acute-angled triangle is defined as a triangle where all three interior angles are less than 90∘90^\circ.

In examining the visual depiction of the triangle provided in the problem, we need to see if it appears to satisfy this property. The assessment relies on observing the triangle's structure shown in the drawing and noting any geometric indications suggesting angle types.

Given the information from the drawing, if all angles seem to satisfy the condition of being less than 90∘90^\circ, then by definition, the triangle is an acute-angled triangle.

Conclusively, the answer to whether the triangle is acute-angled based on provided visual assessment and inherent assumptions in its illustration is: Yes.

Answer:

Yes

Video Solution
Exercise #2

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 #3

Given the values of the sides of a triangle, is it a triangle with different sides?

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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

Video Solution
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

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

Frequently Asked Questions

Everything you need to know about Types of Triangles

What are the 6 main types of triangles students need to know?

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The six main types are: 1) Equilateral (all sides equal), 2) Isosceles (two sides equal), 3) Scalene (all sides different), 4) Right (one 90° angle), 5) Acute (all angles less than 90°), and 6) Obtuse (one angle greater than 90°). These classifications help identify triangle properties and solve geometry problems.

How do you classify triangles by their sides?

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Triangles are classified by sides as follows: • Equilateral: All three sides are equal in length • Isosceles: Exactly two sides are equal in length • Scalene: All three sides have different lengths. Measuring and comparing side lengths is the key to this classification method.

What makes a triangle a right triangle?

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A right triangle has exactly one angle that measures 90 degrees (a right angle). The side opposite the right angle is called the hypotenuse and is always the longest side. Right triangles follow the Pythagorean theorem: a² + b² = c².

How do you find missing angles in triangles?

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Use the triangle angle sum property: all interior angles add up to 180°. To find a missing angle: 1) Add the two known angles, 2) Subtract this sum from 180°, 3) The result is your missing angle. For example: if two angles are 60° and 70°, the third angle is 180° - 60° - 70° = 50°.

What is the difference between acute and obtuse triangles?

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An acute triangle has all three angles measuring less than 90°. An obtuse triangle has exactly one angle measuring greater than 90°. The remaining two angles in an obtuse triangle must be acute (less than 90°) since all angles must sum to 180°.

How do you use the Pythagorean theorem with triangles?

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The Pythagorean theorem (a² + b² = c²) applies only to right triangles. 'a' and 'b' are the legs (shorter sides), and 'c' is the hypotenuse (longest side opposite the right angle). Use it to find missing side lengths when you know two sides of a right triangle.

Can you have a triangle with angles of 90°, 60°, and 40°?

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No, this is impossible. The angles 90° + 60° + 40° = 190°, which exceeds the required 180° sum for triangle interior angles. Valid triangle angles must always sum to exactly 180°, no more and no less.

What are the properties of an isosceles triangle?

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An isosceles triangle has: • Two sides of equal length • Two angles of equal measure (base angles) • One line of symmetry through the vertex angle • The equal angles are opposite the equal sides. These properties make isosceles triangles useful in many geometric proofs and real-world applications.

More Types of Triangles Questions

Click on any question to see the complete solution with step-by-step explanations

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

Continue Your Math Journey

Master Types of Triangles first, then advance to these related topics that build on your fraction skills

Topics Learned in Later Sections

AreaThe sides or edges of a triangleTriangle HeightThe Sum of the Interior Angles of a TriangleExterior angles of a triangleObtuse TriangleEquilateral triangleIdentification of an Isosceles TriangleScalene triangleAcute triangleIsosceles triangleThe Area of a TriangleArea of a right triangleArea of Isosceles TrianglesArea of a Scalene TriangleArea of Equilateral TrianglesAreas of Polygons for 7th GradeRight TriangleMedian in a triangleCenter of a Triangle - The Centroid - The Intersection Point of MediansHow do we calculate the area of complex shapes?How to calculate the area of a triangle using trigonometry?All terms in triangle calculationPerimeterTrianglePerimeter of a triangleHow do we calculate the perimeter of polygons?

Practice by Question Type

Choose your preferred learning style and practice format for fraction problems
Applying the formula Calculate The Missing Side based on the formula Finding the size of angles in a triangle Identifying and defining elements Solving an equation by multiplying/dividing both sides Using Pythagoras' theorem