In triangle DEF, if DE = 5 cm, EF = 12 cm, and DF = 13 cm, is triangle DEF a rig

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Question: In triangle DEF, if DE = 5 cm, EF = 12 cm, and DF = 13 cm, is triangle DEF a right triangle? (2019)

Options:

Correct Answer: Yes

Exam Year: 2019

Solution:

Using the Pythagorean theorem, 5^2 + 12^2 = 25 + 144 = 169 = 13^2. Thus, triangle DEF is a right triangle.

In triangle DEF, if DE = 5 cm, EF = 12 cm, and DF = 13 cm, is triangle DEF a right triangle? (2019)

In triangle DEF, if DE = 5 cm, EF = 12 cm, and DF = 13 cm, is triangle DEF a right triangle? (2019)

Step 1: Identify the lengths of the sides of triangle DEF. They are DE = 5 cm, EF = 12 cm, and DF = 13 cm.
Step 2: Recall 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 other two sides.
Step 3: Identify the longest side, which is DF = 13 cm. This will be our hypotenuse.
Step 4: Calculate the square of DE: 5^2 = 25.
Step 5: Calculate the square of EF: 12^2 = 144.
Step 6: Add the squares of DE and EF: 25 + 144 = 169.
Step 7: Calculate the square of DF: 13^2 = 169.
Step 8: Compare the results from Step 6 and Step 7. Since 169 = 169, the condition of the Pythagorean theorem is satisfied.
Step 9: Conclude that 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.