Question: In triangle GHI, if GH = 5 cm, HI = 12 cm, and GI = 13 cm, 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, 5² + 12² = 25 + 144 = 169 = 13², thus triangle GHI is a right triangle.
In triangle GHI, if GH = 5 cm, HI = 12 cm, and GI = 13 cm, is triangle GHI a rig
Practice Questions
Q1
In triangle GHI, if GH = 5 cm, HI = 12 cm, and GI = 13 cm, 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 = 5 cm, HI = 12 cm, and GI = 13 cm, is triangle GHI a right triangle?
Step 1: Identify the lengths of the sides of triangle GHI. They are GH = 5 cm, HI = 12 cm, and GI = 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 GI = 13 cm. This will be our hypotenuse.
Step 4: Calculate the square of GH: 5² = 25.
Step 5: Calculate the square of HI: 12² = 144.
Step 6: Add the squares of GH and HI: 25 + 144 = 169.
Step 7: Calculate the square of GI: 13² = 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 GHI is a right triangle.
Pythagorean Theorem – 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 Classification – Triangles can be classified based on their angles, with right triangles having one angle equal to 90 degrees.
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