Triangle Practice Problems & Worksheets - Free Online

Master triangle types, angles, area, perimeter, and congruence with step-by-step practice problems. Perfect for students learning geometry fundamentals.

📚Master Triangle Concepts with Interactive Practice
  • Identify equilateral, isosceles, right, and scalene triangles by their properties
  • Calculate missing angles using the 180-degree angle sum rule
  • Find triangle area using base × height ÷ 2 formula
  • Determine triangle perimeter by adding all three side lengths
  • Apply congruence theorems (SSS, SAS, ASA, SSA) to prove triangles equal
  • Use similarity principles to solve proportional triangle problems

Understanding Triangle

Complete explanation with examples

Triangle

In this article, we will briefly learn everything necessary about triangles and also practice with some exercises!
Let's get started!

Detailed explanation

Practice Triangle

Test your knowledge with 38 quizzes

Calculate the area of the triangle below, if possible.

7.67.67.6444

Examples with solutions for Triangle

Step-by-step solutions included
Exercise #1

Angle A is equal to 30°.
Angle B is equal to 60°.
Angle C is equal to 90°.

Can these angles form a triangle?

Step-by-Step Solution

We must first add the three angles to see if they equal 180 degrees:

30+60+90=180 30+60+90=180

The sum of the angles equals 180, therefore they can form a triangle.

Answer:

Yes

Video Solution
Exercise #2

Complete the sentence:

To find the area of a right triangle, one must multiply ________________ by each other and divide by 2.

Step-by-Step Solution

To solve this problem, begin by identifying the elements involved in calculating the area of a right triangle. In a right triangle, the two sides that form the right angle are known as the legs. These legs act as the base and height of the triangle.

The formula for the area of a triangle is given by:

A=12×base×height A = \frac{1}{2} \times \text{base} \times \text{height}

In the case of a right triangle, the base and height are the two legs. Therefore, the process of finding the area involves multiplying the lengths of the two legs together and then dividing the product by 2.

Based on this analysis, the correct way to complete the sentence in the problem is:

To find the area of a right triangle, one must multiply the two legs by each other and divide by 2.

Answer:

the two legs

Exercise #3

Angle A equals 56°.
Angle B equals 89°.
Angle C equals 17°.

Can these angles make a triangle?

Step-by-Step Solution

We add the three angles to see if they are equal to 180 degrees:

56+89+17=162 56+89+17=162

The sum of the given angles is not equal to 180, so they cannot form a triangle.

Answer:

No.

Video Solution
Exercise #4

Angle A equals 90°.
Angle B equals 115°.
Angle C equals 35°.

Can these angles form a triangle?

Step-by-Step Solution

We add the three angles to see if they are equal to 180 degrees:

90+115+35=240 90+115+35=240
The sum of the given angles is not equal to 180, so they cannot form a triangle.

Answer:

No.

Video Solution
Exercise #5

Calculate the area of the following triangle:

444555AAABBBCCCEEE

Step-by-Step Solution

The formula for calculating the area of a triangle is:

(the side * the height from the side down to the base) /2

That is:

BC×AE2 \frac{BC\times AE}{2}

We insert the existing data as shown below:

4×52=202=10 \frac{4\times5}{2}=\frac{20}{2}=10

Answer:

10

Video Solution

Frequently Asked Questions

Everything you need to know about Triangle

What are the 4 main types of triangles and their properties?

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The four main types are: 1) Equilateral - all sides and angles equal (60° each), 2) Isosceles - two equal sides and two equal base angles, 3) Right - one 90° angle with two legs and hypotenuse, 4) Scalene - all sides different lengths.

How do you find the area of a triangle step by step?

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Use the formula: Area = (base × height) ÷ 2. First identify the base (any side) and corresponding height (perpendicular distance from opposite vertex to base). For right triangles, multiply the two legs and divide by 2.

Why do triangle angles always add up to 180 degrees?

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This is a fundamental geometric property. In any triangle, the three interior angles must sum to exactly 180°. This rule helps you find missing angles when you know the other two angles.

What is the difference between congruent and similar triangles?

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Congruent triangles have identical angles AND side lengths - they're exactly the same size. Similar triangles have the same angles but proportional sides - they're the same shape but different sizes.

How do you calculate triangle perimeter for different triangle types?

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Perimeter equals the sum of all three sides: • Equilateral: 3 × side length • Isosceles: 2 × equal side + base • Right triangle: leg₁ + leg₂ + hypotenuse • Scalene: side₁ + side₂ + side₃

What are the triangle congruence theorems I need to know?

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The main congruence theorems are: SSS (three sides equal), SAS (two sides and included angle), ASA (two angles and included side), and SSA (two sides and angle opposite larger side). These prove triangles are identical.

How do you identify if a triangle is right angled?

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A right triangle has exactly one 90° angle. You can identify it by: checking if one angle equals 90°, using the Pythagorean theorem (a² + b² = c²), or looking for the characteristic leg-hypotenuse relationship.

What is the special 45-45-90 triangle and its properties?

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This is a right triangle with two 45° angles, making it both right and isosceles. The sides are in the ratio 1:1:√2, where the legs are equal and the hypotenuse is √2 times longer than each leg.

More Triangle Questions

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

Area of a Triangle

Calculate Triangle Area: Find Area with Sides 5, 7, and 8.6 Solve for X in Right Triangle: Given Area 22.5 and Side X+6 Find X in Right Triangle: Area 18.5 and Height 10 Units Find X in a Right Triangle: Given Area 8.375 and Height 2.5 Calculate Triangle Height X: Area 20 and Base 5 Problem

Triangle

Triangle Classification: Analyzing Angles 53°, 117°, and 21° Isosceles Triangle ABC with Parallel Line ED: Investigating Triangle Properties Triangle Classification: Identifying a Shape with Three 60° Angles Calculate Triangle Area: Paint Coverage in 6-Meter Square Playground Calculate Triangle Perimeter: Finding the Sum of Sides 6, 8, and 10

Perimeter of a Triangle

Calculate Triangle Perimeter: Finding the Sum of Sides 7, 11, and 13 Calculate the Perimeter of an Equilateral Triangle with 5-Unit Sides Find X in an Equilateral Triangle with 33cm Perimeter Calculate the Perimeter: Isosceles Triangle with Sides 6 and Base 4 Solve for X: Finding the Side Length in an Isosceles Triangle with Perimeter 50

Practice by Question Type

Choose your preferred learning style and practice format for fraction problems
Applying the formula Ascertaining whether or not there are errors in the data Calculate The Missing Side based on the formula Calculating in two ways Express using Extended distributive law Finding Area based off Perimeter and Vice Versa How many times does the shape fit inside of another shape? Identifying and defining elements Subtraction or addition to a larger shape Using additional geometric shapes Using congruence and similarity Using decimal fractions Using Pythagoras' theorem Using ratios for calculation Using variables Worded problems Applying the formula Finding Area based off Perimeter and Vice Versa Using Pythagoras' theorem

More Resources and Links

Explore more resources and links related to Triangle
Practice AreaPractice The sides or edges of a trianglePractice Triangle HeightPractice The Sum of the Interior Angles of a TrianglePractice Exterior angles of a trianglePractice PerimeterPractice Types of TrianglesPractice Obtuse TrianglePractice Equilateral trianglePractice Identification of an Isosceles TrianglePractice Scalene trianglePractice Acute trianglePractice Isosceles trianglePractice The Area of a TrianglePractice Area of a right trianglePractice Area of Isosceles TrianglesPractice Area of a Scalene TrianglePractice Area of Equilateral TrianglesPractice Perimeter of a trianglePractice Areas of Polygons for 7th GradePractice Right TrianglePractice Median in a trianglePractice Center of a Triangle - The Centroid - The Intersection Point of MediansPractice How do we calculate the area of complex shapes?Practice How to calculate the area of a triangle using trigonometry?Practice How do we calculate the perimeter of polygons?Practice All terms in triangle calculation