In triangle DEF, if DE = 5 cm, EF = 12 cm, and DF = 13 cm, is triangle DEF a right triangle? (2019)
Practice Questions
1 question
Q1
In triangle DEF, if DE = 5 cm, EF = 12 cm, and DF = 13 cm, is triangle DEF a right triangle? (2019)
Yes
No
Cannot be determined
Only if angle D is 90 degrees
Using the Pythagorean theorem, 5^2 + 12^2 = 25 + 144 = 169 = 13^2. Thus, triangle DEF is a right triangle.
Questions & Step-by-step Solutions
1 item
Q
Q: In triangle DEF, if DE = 5 cm, EF = 12 cm, and DF = 13 cm, is triangle DEF a right triangle? (2019)
Solution: Using the Pythagorean theorem, 5^2 + 12^2 = 25 + 144 = 169 = 13^2. Thus, triangle DEF is a right triangle.
Steps: 9
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.
