Scalene Triangle Practice Problems and Exercises

Master scalene triangles with step-by-step practice problems. Learn to identify and solve scalene triangle exercises with detailed solutions and examples.

📚What You'll Practice with Scalene Triangles
  • Identify scalene triangles by examining side lengths and properties
  • Distinguish scalene triangles from isosceles and equilateral triangles
  • Calculate perimeter and area of scalene triangles using given measurements
  • Solve real-world problems involving scalene triangle applications
  • Apply triangle inequality theorem to verify scalene triangle existence
  • Classify triangles based on side lengths and angle measures

Understanding Scalene triangle

Complete explanation with examples

Definition of Scalene Triangle

An scalene triangle is a triangle that has all its sides of different lengths.

Detailed explanation

Practice Scalene triangle

Test your knowledge with 20 quizzes

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

Examples with solutions for Scalene triangle

Step-by-step solutions included
Exercise #1

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 #2

In a right triangle, the two sides that form a right angle are called...?

Step-by-Step Solution

In a right triangle, there are specific terms for the sides. The two sides that form the right angle are referred to as the legs of the triangle. To differentiate, the side opposite the right angle is called the hypotenuse, which is distinct due to being the longest side. Hence, in response to the problem, the sides forming the right angle are correctly identified as Legs.

Answer:

Legs

Exercise #3

In a right triangle, the side opposite the right angle is called....?

Step-by-Step Solution

The problem requires us to identify the side of a right triangle that is opposite to its right angle.
In right triangles, one of the most crucial elements to recognize is the presence of a right angle (90 degrees).
The side that is directly across or opposite the right angle is known as the hypotenuse. It is also the longest side of a right triangle.
Therefore, when asked for the side opposite the right angle in a right triangle, the correct term is the hypotenuse.

Selection from the given choices corroborates our analysis:

  • Choice 1: Leg - In the context of right triangles, the "legs" are the two sides that form the right angle, not the side opposite to it.
  • Choice 2: Hypotenuse - This is the correct identification for the side opposite the right angle.

Therefore, the correct answer is Hypotenuse \text{Hypotenuse} .

Answer:

Hypotenuse

Exercise #4

Fill in the blanks:

In an isosceles triangle, the angle between two ___ is called the "___ angle".

Step-by-Step Solution

In order to solve this problem, we need to understand the basic properties of an isosceles triangle.

An isosceles triangle has two sides that are equal in length, often referred to as the "legs" of the triangle. The angle formed between these two equal sides, which are sometimes referred to as the "sides", is called the "vertex angle" or sometimes more colloquially as the "main angle".

When considering the vocabulary of the given multiple-choice answers, choice 2: sides,mainsides, main accurately fills the blanks, as the angle formed between the two equal sides can indeed be referred to as the "main angle".

Therefore, the correct answer to the problem is: sides,mainsides, main.

Answer:

sides, main

Exercise #5

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.

Frequently Asked Questions

What is a scalene triangle and how do I identify one?

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A scalene triangle is a triangle where all three sides have different lengths. To identify one, measure or compare all three sides - if no two sides are equal, it's a scalene triangle.

What's the difference between scalene, isosceles, and equilateral triangles?

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• Scalene triangle: All three sides have different lengths • Isosceles triangle: Two sides have equal lengths • Equilateral triangle: All three sides have equal lengths

How do you find the perimeter of a scalene triangle?

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To find the perimeter of a scalene triangle, add all three side lengths together. Since all sides are different, you simply calculate: Perimeter = side a + side b + side c.

Can a scalene triangle be a right triangle?

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Yes, a scalene triangle can be a right triangle. A triangle can be classified by both its sides (scalene, isosceles, equilateral) and its angles (acute, right, obtuse) independently.

What are some real-world examples of scalene triangles?

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Real-world scalene triangles include: 1. Roof trusses in construction 2. Triangular road signs with unequal sides 3. Mountain peaks viewed from the side 4. Sail shapes on boats

How do you prove three sides can form a scalene triangle?

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Use the triangle inequality theorem: the sum of any two sides must be greater than the third side. Check all three combinations: a+b>c, a+c>b, and b+c>a.

What formulas work for calculating scalene triangle area?

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For scalene triangles, you can use: • Heron's formula: √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2 • Base × height ÷ 2 (if height is known) • ½ab sin(C) using two sides and included angle

Are scalene triangles harder to work with than other triangles?

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Scalene triangles require more careful calculation since no sides or angles are equal, but they follow the same geometric principles. With practice, solving scalene triangle problems becomes straightforward.

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