Question: In triangle GHI, if GH = 12 cm, HI = 16 cm, and GI = 20 cm, is triangle GHI a right triangle?
Options:
Yes
No
Only if angle G is 90 degrees
Only if angle H is 90 degrees
Correct Answer: Yes
Solution:
Using the Pythagorean theorem, 12² + 16² = 144 + 256 = 400 = 20², so triangle GHI is a right triangle.
In triangle GHI, if GH = 12 cm, HI = 16 cm, and GI = 20 cm, is triangle GHI a ri
Practice Questions
Q1
In triangle GHI, if GH = 12 cm, HI = 16 cm, and GI = 20 cm, is triangle GHI a right triangle?
Yes
No
Only if angle G is 90 degrees
Only if angle H is 90 degrees
Questions & Step-by-Step Solutions
In triangle GHI, if GH = 12 cm, HI = 16 cm, and GI = 20 cm, is triangle GHI a right triangle?
Step 1: Identify the lengths of the sides of triangle GHI. They are GH = 12 cm, HI = 16 cm, and GI = 20 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 GI = 20 cm. This will be our hypotenuse.
Step 4: Calculate the square of GH: 12² = 144.
Step 5: Calculate the square of HI: 16² = 256.
Step 6: Add the squares of GH and HI: 144 + 256 = 400.
Step 7: Calculate the square of GI: 20² = 400.
Step 8: Compare the sum from Step 6 (400) with the square of GI from Step 7 (400).
Step 9: Since 400 = 400, this means triangle GHI satisfies the Pythagorean theorem.
Step 10: 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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