Triangle Practice Problems: Types, Properties & Geometry

Master triangle types, angle calculations, and geometric properties with interactive practice problems. Build confidence in equilateral, isosceles, right, and scalene triangles.

📚What You'll Master in Triangle Practice
  • Identify and classify equilateral, isosceles, right, and scalene triangles
  • Calculate missing angles using the 180-degree angle sum property
  • Apply Pythagorean theorem to solve right triangle problems
  • Recognize special properties of each triangle type
  • Solve real-world problems involving triangle measurements
  • Understand relationships between sides, angles, and triangle classification

Understanding Triangle

Complete explanation with examples

Geometric shapes

There is a wide variety of geometric shapes, which you can read about in detail:

Triangle

Rectangle

Trapezoid

Parallelogram

kite

Rhombus

Diagram displaying eight geometric shapes: Triangle, Square, Rectangle, Circle, Parallelogram, Trapezoid, Rhombus, and Kite. Each shape is labeled in English beneath it.

Detailed explanation

Practice Triangle

Test your knowledge with 48 quizzes

Look at the parallelogram in the figure.

h = 6

What is the area of the parallelogram?

131313hhhAAABBBCCCDDD

Examples with solutions for Triangle

Step-by-step solutions included
Exercise #1

ABDC is a deltoid.

AB = BD

DC = CA

AD = 12 cm

CB = 16 cm

Calculate the area of the deltoid.

161616121212CCCAAABBBDDD

Step-by-Step Solution

First, let's recall the formula for the area of a rhombus:

(Diagonal 1 * Diagonal 2) divided by 2

Now we will substitute the known data into the formula, giving us the answer:

(12*16)/2
192/2=
96

Answer:

96 cm²

Video Solution
Exercise #2

The trapezoid ABCD is shown below.

AB = 2.5 cm

DC = 4 cm

Height (h) = 6 cm

Calculate the area of the trapezoid.

2.52.52.5444h=6h=6h=6AAABBBCCCDDD

Step-by-Step Solution

First, let's remind ourselves of the formula for the area of a trapezoid:

A=(Base + Base) h2 A=\frac{\left(Base\text{ }+\text{ Base}\right)\text{ h}}{2}

We substitute the given values into the formula:

(2.5+4)*6 =
6.5*6=
39/2 = 
19.5

Answer:

1912 19\frac{1}{2}

Video Solution
Exercise #3

The trapezoid ABCD is shown below.

Base AB = 6 cm

Base DC = 10 cm

Height (h) = 5 cm

Calculate the area of the trapezoid.

666101010h=5h=5h=5AAABBBCCCDDD

Step-by-Step Solution

First, we need to remind ourselves of how to work out the area of a trapezoid:

(Base+Base)h2=Area \frac{(Base+Base)\cdot h}{2}=Area

Now let's substitute the given data into the formula:

(10+6)*5 =
2

Let's start with the upper part of the equation:

16*5 = 80

80/2 = 40

Answer:

40 cm²

Video Solution
Exercise #4

Shown below is the deltoid ABCD.

The diagonal AC is 8 cm long.

The area of the deltoid is 32 cm².

Calculate the diagonal DB.

S=32S=32S=32888AAABBBCCCDDD

Step-by-Step Solution

First, we recall the formula for the area of a kite: multiply the lengths of the diagonals by each other and divide the product by 2.

We substitute the known data into the formula:

 8DB2=32 \frac{8\cdot DB}{2}=32

We reduce the 8 and the 2:

4DB=32 4DB=32

Divide by 4

DB=8 DB=8

Answer:

8 cm

Video Solution
Exercise #5

Look at the rectangle below.

Side AB is 2 cm long and side BC has a length of 7 cm.

What is the perimeter of the rectangle?
222777AAABBBCCCDDD

Step-by-Step Solution

Given that in a rectangle every pair of opposite sides are equal to each other, we can state that:

AB=CD=2 AB=CD=2

AD=BC=7 AD=BC=7

Now we can add all the sides together and find the perimeter:

2+7+2+7=4+14=18 2+7+2+7=4+14=18

Answer:

18 cm

Video Solution

Frequently Asked Questions

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 a hypotenuse, 4) Scalene - all sides and angles different from each other.

How do you find a missing angle in any triangle?

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Use the triangle angle sum property: all angles in a triangle add up to 180°. If you know two angles, subtract their sum from 180° to find the third angle. For example, if two angles are 60° and 80°, the third angle is 180° - 60° - 80° = 40°.

What makes a right triangle special compared to other triangles?

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A right triangle has one 90° angle formed by two perpendicular sides called legs. The side opposite the right angle is the hypotenuse (longest side). Right triangles follow the Pythagorean theorem: a² + b² = c², where c is the hypotenuse.

How can you tell if a triangle is isosceles just by looking at it?

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An isosceles triangle has two equal sides (legs) and two equal base angles. The height from the vertex angle to the base also serves as the median and angle bisector. If you see two sides that appear equal or two angles that look the same, it's likely isosceles.

What's the difference between equilateral and isosceles triangles?

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Equilateral triangles have all three sides equal and all three angles equal to 60°. Isosceles triangles have only two equal sides and two equal angles. Every equilateral triangle is also isosceles, but not every isosceles triangle is equilateral.

Why do all triangle angles always add up to 180 degrees?

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This is a fundamental property of Euclidean geometry. When you draw any triangle on a flat surface, the three interior angles will always sum to exactly 180°. This rule helps us solve for unknown angles and is essential for triangle classification and problem-solving.

How do you solve triangle problems step by step?

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Follow these steps: 1) Identify what type of triangle you have, 2) List the given information (sides, angles), 3) Determine what you need to find, 4) Apply the appropriate formula or property (angle sum, Pythagorean theorem, etc.), 5) Solve algebraically, 6) Check your answer makes sense.

What are common mistakes students make with triangle problems?

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Common errors include: forgetting that angles must sum to 180°, confusing triangle types, incorrectly applying the Pythagorean theorem to non-right triangles, mixing up which side is the hypotenuse, and not checking if their calculated angles or sides create a valid triangle.

More Triangle Questions

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