Question: In triangle DEF, if DE = 8 cm, EF = 6 cm, and DF = 10 cm, is triangle DEF a right triangle?
Options:
Yes
No
Cannot be determined
Only if angle D is 90 degrees
Correct Answer: Yes
Solution:
Using the Pythagorean theorem: 8² + 6² = 64 + 36 = 100 = 10², so triangle DEF is a right triangle.
In triangle DEF, if DE = 8 cm, EF = 6 cm, and DF = 10 cm, is triangle DEF a righ
Practice Questions
Q1
In triangle DEF, if DE = 8 cm, EF = 6 cm, and DF = 10 cm, is triangle DEF a right triangle?
Yes
No
Cannot be determined
Only if angle D is 90 degrees
Questions & Step-by-Step Solutions
In triangle DEF, if DE = 8 cm, EF = 6 cm, and DF = 10 cm, is triangle DEF a right triangle?
Step 1: Identify the lengths of the sides of triangle DEF. They are DE = 8 cm, EF = 6 cm, and DF = 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 triangle DEF. Here, DF = 10 cm is the longest side.
Step 4: Calculate the square of DE (8 cm) and EF (6 cm). So, 8² = 64 and 6² = 36.
Step 5: Add the squares of DE and EF together: 64 + 36 = 100.
Step 6: Calculate the square of DF (10 cm): 10² = 100.
Step 7: Compare the results from Step 5 and Step 6. Since 100 (from DE and EF) equals 100 (from DF), the condition of the Pythagorean theorem is satisfied.
Step 8: Conclude that triangle DEF is a right triangle.
Pythagorean Theorem – A mathematical principle 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 Inequality Theorem – A principle that states the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
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