In triangle DEF, if DE = 6 cm, EF = 8 cm, and DF = 10 cm, is triangle DEF a righ
Practice Questions
Q1
In triangle DEF, if DE = 6 cm, EF = 8 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 = 6 cm, EF = 8 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 = 6 cm, EF = 8 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 squares of the lengths of the sides: DE² = 6² = 36, EF² = 8² = 64, and DF² = 10² = 100.
Step 5: Add the squares of the two shorter sides: 36 + 64 = 100.
Step 6: Compare the sum from Step 5 with the square of the longest side from Step 4: 100 = 100.
Step 7: Since the equation holds true, triangle DEF satisfies the Pythagorean theorem, confirming it is a right triangle.
