Grade 8 Maths Archives - Maths At Sharp - Free Printable

It looks like you've uploaded a worksheet titled "Worksheet 13: Pythagoras" from SHARP, which is part of a mathematics curriculum (likely for Grade 9). The worksheet has two main questions related to the Pythagorean Theorem.

Let’s go through each question and solve them step by step, with explanations.

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Question 1: Which of the following triangles can you use Pythagoras with?

There are four triangles shown:

- Triangle A: An acute triangle (no right angle).
- Triangle B: A right triangle (has a small square in the corner indicating a right angle).
- Triangle C: Another acute triangle (no right angle).
- Triangle D: A right triangle (has a right-angle symbol).

#### ✔ Answer:
You can only use the Pythagorean Theorem on right-angled triangles. The theorem states:

> In a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides:
>
> $$
> a^2 + b^2 = c^2
> $$

So, only triangles with a right angle qualify.

Thus, Triangles B and D can be used with the Pythagorean Theorem.

> ✔ Answer: B and D

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Question 2: Given the triangles below, give the formula of Pythagoras for each triangle.

We have four right-angled triangles labeled A, B, C, and D. Each has sides labeled with letters.

Let’s analyze each one:

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#### Triangle A:
- Right angle at the bottom left.
- Sides: $ a $, $ b $, $ c $
- Hypotenuse is the side opposite the right angle → that's $ c $
- So, the Pythagorean formula is:
$$
a^2 + b^2 = c^2
$$

✔ Answer: $ a^2 + b^2 = c^2 $

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#### Triangle B:
- Right angle at the top right.
- Sides: $ x $, $ y $, $ z $
- Hypotenuse is the side opposite the right angle → that's $ z $
- So:
$$
x^2 + y^2 = z^2
$$

✔ Answer: $ x^2 + y^2 = z^2 $

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#### Triangle C:
- Right angle at the bottom left.
- Sides: $ p $, $ q $, $ r $
- Hypotenuse is $ r $ (opposite the right angle)
- So:
$$
p^2 + q^2 = r^2
$$

✔ Answer: $ p^2 + q^2 = r^2 $

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#### Triangle D:
- Right angle at the top right.
- Sides: $ m $, $ n $, $ o $
- Hypotenuse is $ o $ (opposite the right angle)
- So:
$$
m^2 + n^2 = o^2
$$

✔ Answer: $ m^2 + n^2 = o^2 $

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✔ Final Answers:

#### Question 1:
B and D — These are the right-angled triangles where Pythagoras can be applied.

#### Question 2:
- A: $ a^2 + b^2 = c^2 $
- B: $ x^2 + y^2 = z^2 $
- C: $ p^2 + q^2 = r^2 $
- D: $ m^2 + n^2 = o^2 $

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🔍 Explanation Summary:

- The Pythagorean Theorem applies only to right-angled triangles.
- The hypotenuse is always the longest side and is opposite the right angle.
- The formula is always: (leg₁)² + (leg₂)² = (hypotenuse)²

This worksheet helps students identify when the theorem applies and how to write the correct equation based on labeling.

Let me know if you'd like this turned into a printable answer sheet or need help solving actual numerical problems using Pythagoras!