Triangles Unit Test
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Question
Use the image to answer the question.
A triangle has the vertices labeled upper M upper N upper O. Upper N upper O is labeled m, upper M upper N is labeled o, and upper O upper M is labeled n. Angle upper N measures 62 degrees and angle upper M measures 28 degrees.
What is the relationship of the sides in this triangle based on the Pythagorean Theorem?
(1 point)
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m^2+n^2=?????
Based on the Pythagorean Theorem, the relationship between the sides of a right triangle is that the square of the length of the hypotenuse (in this case, side m) is equal to the sum of the squares of the lengths of the other two sides (in this case, sides n and o).
So, in this triangle, the relationship would be m^2 = n^2 + o^2.
To determine the relationship of the sides in this triangle based on the Pythagorean Theorem, we need to understand that 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 lengths of the other two sides.
In this triangle, we are given that angle N measures 62 degrees and angle M measures 28 degrees. Since the sum of the interior angles in any triangle is 180 degrees, we can deduce that angle O measures 180 - 62 - 28 = 90 degrees.
Therefore, triangle MON is a right triangle, with angle O being the right angle. We can conclude that line segment MO is the hypotenuse.
Now, based on the Pythagorean Theorem, the relationship of the sides in this triangle can be expressed as:
m^2 + n^2 = MO^2
So, the relationship of the sides in this triangle based on the Pythagorean Theorem is that the sum of the squares of the lengths of the two legs (m^2 and n^2) is equal to the square of the length of the hypotenuse (MO^2).
To determine the relationship of the sides in the triangle based on the Pythagorean Theorem, we need to know the lengths of the sides referred to as "m" and "n" in the given triangle.
However, the given information only provides the measures of angles N and M. To determine the side lengths, we need additional information such as the lengths of other sides or the values of other angles.
Without any additional information, we cannot directly determine the relationship of the sides using the Pythagorean Theorem.