Kurikulum Merdeka Matematika Kelas 8 Bab 2 Teorema Pythagoras

Summary

In this educational video, the host explains the Pythagorean Theorem and its applications for right-angled triangles. The video covers the formula c² = a² + b², demonstrating how to find the hypotenuse and other sides using real-life examples. It also introduces Pythagorean triples, which simplify calculations, and discusses special triangles like the isosceles right triangle and the 30-60-90 triangle. The content is designed to help viewers understand these mathematical concepts with step-by-step explanations and examples, making learning math more accessible and engaging.

Takeaways

• 😀 Pythagoras' Theorem states that in a right triangle, the square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides (a² + b² = c²).
• 😀 To find the longest side (hypotenuse) in a right triangle, use the formula c² = a² + b², and solve for c.
• 😀 In a right triangle, the hypotenuse is always opposite the right angle.
• 😀 The Pythagorean theorem can be rearranged to find a missing leg (side): a² = c² - b².
• 😀 Example problem: Given the base of a right triangle as 5 cm and height as 12 cm, the hypotenuse (c) is found by calculating the square root of 169, which equals 13 cm.
• 😀 Another example: If the hypotenuse is 2.9 cm and the height is 2.1 cm, the base is 2 cm after solving using the rearranged Pythagorean formula.
• 😀 Pythagorean Triples are sets of three whole numbers (a, b, c) that satisfy the Pythagorean theorem. These are useful for quickly solving problems without calculations.
• 😀 The video shows a table of common Pythagorean Triples, encouraging memorization for faster problem solving.
• 😀 Special Right Triangles include the 'Isosceles Right Triangle' (45°-45°-90°) where the hypotenuse is equal to the leg multiplied by √2.
• 😀 Another special triangle is the '30°-60°-90° Triangle,' where the hypotenuse is twice the shorter leg, and the other leg is the shorter leg multiplied by √3.

Q & A

What is the Pythagorean Theorem?

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. This is represented as c² = a² + b².

How can you determine the longest side in a right triangle?

The longest side, also known as the hypotenuse, is always opposite the right angle (90°) in a right triangle. You can identify it by looking for the side opposite the 90° angle.

What is the formula used to find the hypotenuse when the other two sides are known?

The formula to find the hypotenuse (c) is c² = a² + b². After substituting the values of a and b, take the square root of the result to find c.

How do you calculate the hypotenuse if the sides are 5 cm and 12 cm?

Using the formula c² = a² + b², substitute the values: 5² + 12² = 25 + 144 = 169. Then, take the square root of 169, which equals 13 cm.

How do you find the base of a triangle when the hypotenuse and height are known?

To find the base (a) when the hypotenuse (c) and height (b) are known, use the formula a² = c² - b². For example, if c = 2.9 cm and b = 2.1 cm, then a² = 2.9² - 2.1² = 8.41 - 4.41 = 4, so a = √4 = 2 cm.

What is a Pythagorean triple?

A Pythagorean triple is a set of three positive integers a, b, and c that satisfy the equation a² + b² = c². These triples can be memorized to simplify calculations.

Can you provide an example of a Pythagorean triple?

An example of a Pythagorean triple is (3, 4, 5). This means 3² + 4² = 9 + 16 = 25, and the hypotenuse (c) is 5.

What is a special right triangle?

A special right triangle includes two types: the 45°-45°-90° triangle (isosceles right triangle) and the 30°-60°-90° triangle. These triangles have specific properties that can simplify calculations.

How do you calculate the hypotenuse in a 45°-45°-90° triangle?

In a 45°-45°-90° triangle, the legs (sides opposite the 45° angles) are equal. The hypotenuse is the leg multiplied by √2. For example, if the legs are 5 cm, the hypotenuse will be 5√2 cm.

How do you calculate the sides of a 30°-60°-90° triangle?

In a 30°-60°-90° triangle, the side opposite the 30° angle is half the length of the hypotenuse, and the side opposite the 60° angle is the length of the side opposite the 30° angle multiplied by √3.