In triangle PQR, if PQ = 6 cm, PR = 8 cm, and QR = 10 cm, is triangle PQR a righ

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Question: In triangle PQR, if PQ = 6 cm, PR = 8 cm, and QR = 10 cm, is triangle PQR a right triangle?

Options:

Correct Answer: Yes

Solution:

Using the Pythagorean theorem, if QR² = PQ² + PR², then 10² = 6² + 8², which gives 100 = 36 + 64 = 100. Therefore, triangle PQR is a right triangle.

In triangle PQR, if PQ = 6 cm, PR = 8 cm, and QR = 10 cm, is triangle PQR a right triangle?

In triangle PQR, if PQ = 6 cm, PR = 8 cm, and QR = 10 cm, is triangle PQR a right triangle?

Step 1: Identify the lengths of the sides of triangle PQR. We have PQ = 6 cm, PR = 8 cm, and QR = 10 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 hypotenuse. In triangle PQR, QR is the longest side, so it is the hypotenuse.
Step 4: Calculate QR squared. QR = 10 cm, so QR² = 10² = 100.
Step 5: Calculate PQ squared. PQ = 6 cm, so PQ² = 6² = 36.
Step 6: Calculate PR squared. PR = 8 cm, so PR² = 8² = 64.
Step 7: Add PQ² and PR² together. We have 36 + 64 = 100.
Step 8: Compare QR² with the sum of PQ² and PR². We found QR² = 100 and PQ² + PR² = 100.
Step 9: Since QR² equals PQ² + PR², triangle PQR is a right triangle.

Pythagorean Theorem – The theorem states that 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 – Understanding how to classify triangles based on their side lengths and angles, particularly identifying right triangles.