Question

1. 22) 23) 24) state if each triangle is a right triangle.

Explanation:

Step1: Recall the Pythagorean theorem

The Pythagorean theorem states that for a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\).

Step2: Check triangle 21)

Let \(a = 9\), \(b = 12\), \(c = 15\).
Calculate \(a^{2}+b^{2}\): \(9^{2}+12^{2}=81 + 144=225\).
Calculate \(c^{2}\): \(15^{2}=225\).
Since \(9^{2}+12^{2}=15^{2}\), triangle 21) is a right - triangle.

Step3: Check triangle 22)

Let \(a = 3\), \(b = 8\), \(c = 10\).
Calculate \(a^{2}+b^{2}\): \(3^{2}+8^{2}=9 + 64 = 73\).
Calculate \(c^{2}\): \(10^{2}=100\).
Since \(3^{2}+8^{2}
eq10^{2}\), triangle 22) is not a right - triangle.

Step4: Check triangle 23)

Let \(a = 3\), \(b = 4\), \(c = 5\).
Calculate \(a^{2}+b^{2}\): \(3^{2}+4^{2}=9+16 = 25\).
Calculate \(c^{2}\): \(5^{2}=25\).
Since \(3^{2}+4^{2}=5^{2}\), triangle 23) is a right - triangle.

Answer:

1. is a right - triangle. 22) is not a right - triangle. 23) is a right - triangle.