In this article, we will briefly learn everything necessary about triangles and also practice with some exercises!
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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
Practice Triangle
Test your knowledge with 37 quizzes
Calculate the area of the following triangle:
Examples with solutions for Triangle
Step-by-step solutions included
Exercise #1
The triangle ABC is given below.
AC = 10 cm
AD = 3 cm
BC = 11.6 cm
What is the area of the triangle?
Step-by-Step Solution
The triangle we are looking at is the large triangle - ABC
The triangle is formed by three sides AB, BC, and CA.
Now let's remember what we need for the calculation of a triangular area:
(side x the height that descends from the side)/2
Therefore, the first thing we must find is a suitable height and side.
We are given the side AC, but there is no descending height, so it is not useful to us.
The side AB is not given,
And so we are left with the side BC, which is given.
From the side BC descends the height AD (the two form a 90-degree angle).
It can be argued that BC is also a height, but if we delve deeper it seems that CD can be a height in the triangle ADC,
and BD is a height in the triangle ADB (both are the sides of a right triangle, therefore they are the height and the side).
As we do not know if the triangle is isosceles or not, it is also not possible to know if CD=DB, or what their ratio is, and this theory fails.
Let's remember again the formula for triangular area and replace the data we have in the formula:
(side* the height that descends from the side)/2
Now we replace the existing data in this formula:
Answer:
17.4
Video Solution
Exercise #2
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:
The sum of the given angles is not equal to 180, so they cannot form a triangle.
Answer:
No.
Video Solution
Exercise #3
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:
The sum of the angles equals 180, therefore they can form a triangle.
Answer:
Yes
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:
The sum of the given angles is not equal to 180, so they cannot form a triangle.
Answer:
No.
Video Solution
Exercise #5
What is the area of the given triangle?
Step-by-Step Solution
This question is a bit confusing. We need start by identifying which parts of the data are relevant to us.
Remember the formula for the area of a triangle:
The height is a straight line that comes out of an angle and forms a right angle with the opposite side.
In the drawing we have a height of 6.
It goes down to the opposite side whose length is 5.
And therefore, these are the data points that we will use.
We replace in the formula:
Answer:
15
Video Solution
Frequently Asked Questions
What are the 4 main types of triangles and their properties?
+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?
+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?
+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?
+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?
+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?
+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?
+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?
+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.