Pythagorean Theorem Proofs Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
1 of 51 of 5 Items
Question
Use the image to answer the question.
A right-angled triangle has the vertices labeled upper P upper S upper T. The height upper S upper T is labeled p; the base upper T upper P is labeled s; and the hypotenuse upper P upper S is labeled t.
Which equation is a true equation based on the right triangle shown?
Option 1: p2+t2=s2
Option 2: p2+s2=t2
Option 3: There is not enough information about the triangle to write an equation.
Enter "1", "2", or "3".
(1 point)
wrong
Option 2: p2+s2=t2
The correct answer is Option 2: p^2 + s^2 = t^2.
To answer this question, we need to use the Pythagorean Theorem, which states that in a right-angled 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.
In the given triangle, let's label the hypotenuse as 'c' instead of 't', to follow the traditional notation. So we have:
c^2 = a^2 + b^2
In the given options, we have p as the height (opposite the right angle), s as the base, and t as the hypotenuse. So we need to figure out which equation represents the Pythagorean Theorem in terms of p, s, and t.
Let's compare the options to the Pythagorean Theorem equation:
Option 1: p^2 + t^2 = s^2
Option 2: p^2 + s^2 = t^2
Comparing these options to the Pythagorean Theorem equation, we can see that Option 2 matches:
p^2 + s^2 = t^2
Therefore, the correct answer is Option 2.
If a triangle has sides 12, 16, and 20, which length is the length of the hypotenuse?(1 point)
To determine the length of the hypotenuse, we can use the Pythagorean Theorem.
The Pythagorean Theorem states that in a right-angled 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.
In this case, the sides are 12, 16, and 20. We can label the hypotenuse as 'c', and the other two sides as 'a' and 'b'. We want to find the length of the hypotenuse, which is 'c'.
Using the Pythagorean Theorem, we have:
c^2 = a^2 + b^2
Plugging in the values, we have:
c^2 = 12^2 + 16^2
c^2 = 144 + 256
c^2 = 400
Taking the square root of both sides, we have:
c = √400
c = 20
Therefore, the length of the hypotenuse is 20 units.
Triangle GHI
is a right triangle. The length of one leg is 11 and the hypotenuse is 22. What is the length of the other leg? Round your answer to two decimal places.(1 point)
I apologize for the mistake. Let's solve the problem correctly.
According to the Pythagorean Theorem, 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.
Let's label the legs of the right triangle as 'a' and 'b', and the hypotenuse as 'c'.
Given:
Length of leg a: 11
Length of hypotenuse c: 22
Using the Pythagorean Theorem, we can set up the following equation:
a^2 + b^2 = c^2
Plugging in the known values, we have:
11^2 + b^2 = 22^2
Simplifying further:
121 + b^2 = 484
Subtracting 121 from both sides:
b^2 = 363
Taking the square root of both sides:
b ≈ ±19.07
Since the length of a side cannot be negative, the length of the other leg is approximately 19.07 units (rounded to two decimal places).
Therefore, the length of the other leg is approximately 19.07 units.
Triangle GHI is a right triangle. The length of one leg is 11 and the hypotenuse is 22. What is the length of the other leg? Round your answer to two decimal places.(1 point)
Which statement explains the Pythagorean Theorem?(1 point)
Responses
If a triangle is a right triangle, then the sum of the squares of the legs is equal to the square of the hypotenuse.
If a triangle is a right triangle, then the sum of the squares of the legs is equal to the square of the hypotenuse.
If the interior angles of a triangle add up to 180°, then the sum of the legs of the triangle is equal to the square of the hypotenuse.
If the interior angles of a triangle add up to 180 degrees , then the sum of the legs of the triangle is equal to the square of the hypotenuse.
If a triangle is a right triangle, then the sum of the squares of the longest leg and the hypotenuse is equal to the square of the third side.
If a triangle is a right triangle, then the sum of the squares of the longest leg and the hypotenuse is equal to the square of the third side.
If all angles in a triangle are of equal measure, then the length of all sides will be equal.