Question

quiz
apply the pythagorean theorem. find whether each triangle has a right angle.
①
②

Explanation:

Step1: Apply Pythagorean theorem for first triangle

For triangle \(ABC\) with \(a = 18\), \(b=24\), \(c = 30\). Check if \(a^{2}+b^{2}=c^{2}\).
\(18^{2}+24^{2}=324 + 576=900\) and \(30^{2}=900\).

Step2: Apply Pythagorean theorem for second triangle

For triangle \(PQR\) with \(a = 12\), \(b = 13\), \(c=17\). Check if \(a^{2}+b^{2}=c^{2}\).
\(12^{2}+13^{2}=144+169 = 313\) and \(17^{2}=289\).

Answer:

1. The triangle \(ABC\) has a right - angle.
2. The triangle \(PQR\) does not have a right - angle.