Question: In triangle GHI, if GH = 8, HI = 6, and GI = 10, is triangle GHI a right triangle?
Options:
Yes
No
Not enough information
Only if angle G is 90 degrees
Correct Answer: Yes
Solution:
Using the Pythagorean theorem: 8² + 6² = 64 + 36 = 100 = 10², so triangle GHI is a right triangle.
In triangle GHI, if GH = 8, HI = 6, and GI = 10, is triangle GHI a right triangl
Practice Questions
Q1
In triangle GHI, if GH = 8, HI = 6, and GI = 10, is triangle GHI a right triangle?
Yes
No
Not enough information
Only if angle G is 90 degrees
Questions & Step-by-Step Solutions
In triangle GHI, if GH = 8, HI = 6, and GI = 10, is triangle GHI a right triangle?
Step 1: Identify the lengths of the sides of triangle GHI. They are GH = 8, HI = 6, and GI = 10.
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 GI = 10. This will be our hypotenuse.
Step 4: Calculate the square of GH: 8² = 64.
Step 5: Calculate the square of HI: 6² = 36.
Step 6: Add the squares of GH and HI: 64 + 36 = 100.
Step 7: Calculate the square of GI: 10² = 100.
Step 8: Compare the results from Step 6 and Step 7. Since 100 = 100, the condition of the Pythagorean theorem is satisfied.
Step 9: Conclude that triangle GHI 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 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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