In triangle GHI, if GH = 5 cm, HI = 12 cm, and GI = 13 cm, what type of triangle

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Question: In triangle GHI, if GH = 5 cm, HI = 12 cm, and GI = 13 cm, what type of triangle is it?

Options:

Correct Answer: Right

Solution:

Using the Pythagorean theorem, 5^2 + 12^2 = 25 + 144 = 169, which equals 13^2. Therefore, triangle GHI is a right triangle.

In triangle GHI, if GH = 5 cm, HI = 12 cm, and GI = 13 cm, what type of triangle is it?

In triangle GHI, if GH = 5 cm, HI = 12 cm, and GI = 13 cm, what type of triangle is it?

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: 5^2 = 25.
Step 5: Calculate the square of HI: 12^2 = 144.
Step 6: Add the squares of GH and HI: 25 + 144 = 169.
Step 7: Calculate the square of GI: 13^2 = 169.
Step 8: Compare the results from Step 6 and Step 7. Since 169 (from GH and HI) equals 169 (from GI), the triangle satisfies the Pythagorean theorem.
Step 9: Conclude that triangle GHI is a right triangle because it meets the criteria of the Pythagorean theorem.

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.
Types of Triangles – Understanding the classification of triangles based on their side lengths and angles, specifically right, acute, and obtuse triangles.