The measurements 3, 4, and 5 satisfy the converse of the Pythagorean Theorem and therefore form a right triangle. If each measurement is doubled, will the new triangle still be a right triangle? Write an argument that can be used to defend your solution.
What do you know about similar triangles?
Similar triangles have the same shape but a different size
https://www.mathsisfun.com/geometry/triangles-similar.html
exactly. If you cut each side of a triangle in half, do the angles change?
say you have a 6, 8 ,10 triangle
is it a right triangle 2*3 , 2*4 , 2*5
?????
I claim it is same shape, different size.
and if it is the same shape, that right angle is still a right angle.
The angles do not change and it will still be a right triangle
Thank you damon
2*3 , 2*4 , 2*5
square each
4*9 , 4*16 , 4*25
try right angle test
4*9 + 4*16 = 4*25 ????
divide both sides by 4
9 + 16 = 25 sure enough that same old 3,4,5 right triangle, just a little bigger
To determine if doubling the measurements of a right triangle will still form a right triangle, we need to apply the Pythagorean Theorem and assess if the doubled measurements satisfy it.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Mathematically, it can be expressed as:
c^2 = a^2 + b^2
Where:
- c represents the length of the hypotenuse
- a and b represent the lengths of the other two sides
In this case, we have a right triangle with measurements 3, 4, and 5. Let's verify if it satisfies the Pythagorean Theorem:
c^2 = a^2 + b^2
5^2 = 3^2 + 4^2
25 = 9 + 16
25 = 25
Since the equation is true, the measurements 3, 4, and 5 indeed satisfy the Pythagorean Theorem and form a right triangle.
Now, to determine if doubling the measurements will still form a right triangle, let's double each measurement:
2a = 2 * 3 = 6
2b = 2 * 4 = 8
2c = 2 * 5 = 10
Now we can apply the Pythagorean Theorem to the doubled measurements:
(2c)^2 = (2a)^2 + (2b)^2
10^2 = 6^2 + 8^2
100 = 36 + 64
100 = 100
Again, the equation is true. This proves that when you double the measurements of a right triangle, the new triangle formed will also satisfy the Pythagorean Theorem and hence be a right triangle.