In triangle DEF, if DE = 6 cm, DF = 8 cm, and EF = 10 cm, is triangle DEF a righ

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Question: In triangle DEF, if DE = 6 cm, DF = 8 cm, and EF = 10 cm, is triangle DEF a right triangle?

Options:

Correct Answer: Yes

Solution:

By the Pythagorean theorem, if DE^2 + DF^2 = EF^2, then it is a right triangle. 6^2 + 8^2 = 36 + 64 = 100 = 10^2.

In triangle DEF, if DE = 6 cm, DF = 8 cm, and EF = 10 cm, is triangle DEF a right triangle?

In triangle DEF, if DE = 6 cm, DF = 8 cm, and EF = 10 cm, is triangle DEF a right triangle?

Step 1: Identify the lengths of the sides of triangle DEF. We have DE = 6 cm, DF = 8 cm, and EF = 10 cm.
Step 2: Recall the Pythagorean theorem, which states that in a right triangle, the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.
Step 3: Identify the longest side. In this case, EF (10 cm) is the longest side.
Step 4: Calculate the square of each side: DE^2 = 6^2 = 36, DF^2 = 8^2 = 64, and EF^2 = 10^2 = 100.
Step 5: Add the squares of the two shorter sides: 36 + 64 = 100.
Step 6: Compare the sum with the square of the longest side: 100 (from DE^2 + DF^2) equals 100 (from EF^2).
Step 7: Since the two values are equal, triangle DEF is a right triangle.

Pythagorean Theorem – A fundamental principle in geometry that states in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.