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Pythagoras' Law Smart Worksheet

Smart Worksheet · Grade 10 · English

Pythagoras' Law Smart Worksheet

Activity 1: Understanding Pythagoras' Law

Instructions: Read the following statement and write the formula for Pythagoras' Law in your own words. Then, explain what each variable represents.
"In a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides."
Formula: ____________________________________________________________
Explanation of variables:
  • a: _______________________________________________________________
  • b: _______________________________________________________________
  • c: _______________________________________________________________

Activity 2: Identifying Right Triangles

Instructions: For each set of side lengths below, determine whether they can form a right-angled triangle. Show your calculations using Pythagoras' Law.
  1. Sides: 5 cm, 12 cm, 13 cm
Work:

  1. Sides: 7 cm, 24 cm, 25 cm
Work:

  1. Sides: 8 cm, 15 cm, 17 cm
Work:


Activity 3: Solving for the Unknown Side

Instructions: Find the missing side in each right-angled triangle below. Show your work and write your answers with correct units.
  1. a = 9 cm, b = 12 cm, c = ?
Work:

  1. a = ?, b = 5 cm, c = 13 cm
Work:

  1. a = 7 cm, b = ?, c = 25 cm
Work:


Activity 4: Real-Life Application

Instructions: A ladder is leaning against a wall. The bottom of the ladder is 6 meters from the wall, and the ladder reaches a height of 8 meters on the wall. What is the length of the ladder? Draw a diagram and solve for the length. Show all your steps.
Diagram:


| | | | | | | | | | | |

Work:


Activity 5: Creative Challenge

Instructions: Create your own word problem that involves Pythagoras' Law. Write the problem and solve it, showing all your work and the answer.
My problem:

Solution:


Pythagoras' Law Fresh Worksheet

Activity 1: Stating and Visualizing Pythagoras' Law

Instructions: Carefully read the statement below, then write the Pythagoras' Law formula and illustrate a right-angled triangle labeling all sides.
In a right-angled triangle, the area of the square constructed on the hypotenuse is equal to the sum of the areas of the squares constructed on the other two sides.
Formula: ____________________________________________________________
[Image: Draw a right-angled triangle and label the sides as a, b, and c (where c is the hypotenuse)]

Activity 2: True or False

Instructions: Decide whether each statement is true or false. If false, correct the statement.
  1. In any triangle, the Pythagoras' Law always applies.
  1. The hypotenuse is always the longest side in a right-angled triangle.
  1. If

, the triangle must be right-angled.
  1. Pythagoras' Law can be used to find the length of a missing side in a right-angled triangle.

Activity 3: Find the Missing Side

Instructions: Use Pythagoras' Law to find the missing side in each triangle below. Show all your calculations.
  1. a = 6 cm, b = 8 cm, c = ?
Work:

  1. a = ?, b = 9 cm, c = 15 cm
Work:

  1. a = 20 m, b = ?, c = 29 m
Work:


Activity 4: Word Problems

Instructions: Solve the following real-life problems using Pythagoras' Law. Show all your work and write your answers with correct units.
  1. A rectangular television screen measures 48 cm in height and 64 cm in width. What is the length of its diagonal?
Work:

  1. A tree casts a shadow of 12 meters. If the distance from the top of the tree to the end of the shadow is 20 meters, how tall is the tree?
Work:


Activity 5: Pythagorean Triples Investigation

Instructions: A Pythagorean triple consists of three positive integers a, b, and c, such that

. Find two different sets of Pythagorean triples (other than those used in previous activities) and show your calculations.
Set 1: a = _____, b = _____, c = _____
Work:

Set 2: a = _____, b = _____, c = _____
Work:


Activity 6: Create and Solve

Instructions: Create your own word problem that requires the use of Pythagoras' Law to solve. Write your problem and solve it, showing all your work and the answer.
My problem:

Solution:

A right-angled triangle with sides labeled a, b, and c