Question

in each figure create a right triangle. justify your answer.
14.
16.
using the pythagorean theorem. 8.7d

Explanation:

Step1: Apply Pythagorean theorem

For a triangle with sides \(a\), \(b\), \(c\) (\(c\) is the longest side), if \(a^{2}+b^{2}=c^{2}\), then it is a right - triangle.
For the triangle in problem 14: \(a = 6\), \(b=7\), \(c = 10\). Calculate \(a^{2}+b^{2}=6^{2}+7^{2}=36 + 49=85\), and \(c^{2}=10^{2}=100\). Since \(85
eq100\), it is not a right - triangle.
For the triangle in problem 16: \(a = 6\), \(b = 9\), \(c=12\). Calculate \(a^{2}+b^{2}=6^{2}+9^{2}=36+81 = 117\), and \(c^{2}=12^{2}=144\). Since \(117
eq144\), it is not a right - triangle.

Answer:

Neither of the two triangles is a right - triangle. For the triangle with sides \(6\), \(7\), \(10\), \(6^{2}+7^{2}=85
eq10^{2}\). For the triangle with sides \(6\), \(9\), \(12\), \(6^{2}+9^{2}=117
eq12^{2}\).