Mr. ivin's algebra class is learning the pythagorean theorem. he has two students that are auditory learners and are struggling

Question

1 year ago

12

with the concept. what activity would best help them learn the theorem?

2 answers:

GrogVix [38] · Answer 1 · 2023-08-11T05:51:29+03:00

In a right - angled triangle, the square of the hypotenuse of a triangle is equal to the sum of the square of the other two sides.

Step 1: Make a right - angled triangle with base, perpendicular and hypotenuse has length of their side a, b, c respectively.

Step 2: Make squares on the base, perpendicular and hypotenuse with side length a, b and c respectively.

Step 3: Now measure the area of square with side b and a, which are on perpendicular and base of a triangle respectively.

Step 4: Measure the area of the with side c, which is on the hypotenuse of a triangle, area is: $c^{2}$ .

Step 5: Add the area of squares with sides a and b, sum of their area is: $a^{2} + b^{2}$ .

Observation and Result:

We will notice that the area of square with side a and b is equal to the area of square with side c.

⇒ $a^{2} + b^{2} = c^{2}$

∴ The square of the hypotenuse in a right-angled triangle is equal to the sum of the square of the other two sides.

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lord [1] · Answer 2 · 2023-08-11T07:47:00+03:00

In a right triangle, the square of the hypotenuse of the triangle is equal to the sum of the squares of the other two sides.

Construct a right triangle with base, perpendicular and hypotenuse lengths a, b and c respectively.

Create a square with base, perpendicular and hypotenuse sides of lengths a, b and c respectively.

Next, measure the area of the square whose sides b and a are perpendicular and base of the triangle, respectively.

If you measure the area of side c that is the hypotenuse of the triangle, the area is c².

Adding the areas of the squares with sides a and b gives the sum of their area gives a² + b².

Note that the area of the square with sides a and b is equal to the area of the square with side c.

a² + b² = c²

Therefore, the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

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