A triangle, labeled as triangle EGO, is shown. The side lengths are labeled. Side EG is 7 cm, GO is 14 cm, and EO is 13 cm. The vertices are labeled as E, G, and O. The diagram is a standard geometric representation of a triangle with specified side lengths.

Question

Is this a right triangle? Why or Why not?

(1 point)
Responses

Yes, the Pythagorean Theorem holds true using 14 as the hypotenuse
Yes, the Pythagorean Theorem holds true using 14 as the hypotenuse

No, the Pythagorean Theorem does not hold true using any of the sides as the hypotenuse
No, the Pythagorean Theorem does not hold true using any of the sides as the hypotenuse

No, the Pythagorean Theorem does not hold true using 14 as the hypotenuse
No, the Pythagorean Theorem does not hold true using 14 as the hypotenuse

Yes, the Pythagorean Theorem holds true using any of the sides as the hypotenuse

Answer 1

To determine whether triangle EGO is a right triangle, we can use the Pythagorean theorem, which states that in a right 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 two other sides.

In triangle EGO, we have the following side lengths:

• EG = 7 cm
• GO = 14 cm (this will be considered as the hypotenuse)
• EO = 13 cm

Now, we will apply the Pythagorean theorem:

1. Calculate \( 14^2 \): \( 14^2 = 196 \)

2. Calculate \( 7^2 + 13^2 \): \( 7^2 = 49 \) \( 13^2 = 169 \) \( 7^2 + 13^2 = 49 + 169 = 218 \)

Now, we check if \( 14^2 = 7^2 + 13^2 \):

• \( 196 \neq 218 \)

Since the equation does not hold true, triangle EGO is not a right triangle.

Therefore, the correct response is: No, the Pythagorean Theorem does not hold true using 14 as the hypotenuse.