Question: In triangle DEF, if DE = 6, EF = 8, and DF = 10, is triangle DEF a right triangle?
Options:
Yes
No
Not enough information
Only if angle D is 90 degrees
Correct Answer: Yes
Solution:
Using the Pythagorean theorem, 6² + 8² = 36 + 64 = 100 = 10², thus triangle DEF is a right triangle.
In triangle DEF, if DE = 6, EF = 8, and DF = 10, is triangle DEF a right triangl
Practice Questions
Q1
In triangle DEF, if DE = 6, EF = 8, and DF = 10, is triangle DEF a right triangle?
Yes
No
Not enough information
Only if angle D is 90 degrees
Questions & Step-by-Step Solutions
In triangle DEF, if DE = 6, EF = 8, and DF = 10, is triangle DEF a right triangle?
Step 1: Identify the lengths of the sides of triangle DEF. We have DE = 6, EF = 8, and DF = 10.
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 triangle DEF. Here, DF = 10 is the longest side.
Step 4: Calculate the square of the lengths of the two shorter sides: DE² = 6² = 36 and EF² = 8² = 64.
Step 5: Add the squares of the two shorter sides: 36 + 64 = 100.
Step 6: Calculate the square of the longest side: DF² = 10² = 100.
Step 7: Compare the results from Step 5 and Step 6. Since 100 (from the shorter sides) equals 100 (from the longest side), triangle DEF satisfies the Pythagorean theorem.
Step 8: 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.
Triangle Classification – The process of determining the type of triangle based on the lengths of its sides, specifically identifying right triangles using the Pythagorean theorem.
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