Question

prove the triangles below are similar by using slope. slope= type your answer.

Explanation:

Step1: Recall slope formula

The slope formula for a right - triangle (rise over run) is $m=\frac{\text{vertical side}}{\text{horizontal side}}$.

Step2: Calculate slope of first triangle

For the first triangle with vertical side $a = 12$ and horizontal side $b = 10$, the slope $m_1=\frac{12}{10}=\frac{6}{5}$.

Step3: Calculate slope of second triangle

For the second triangle with vertical side $c = 6$ and horizontal side $d = 5$, the slope $m_2=\frac{6}{5}$.

Step4: Compare slopes

Since $m_1=\frac{6}{5}$ and $m_2=\frac{6}{5}$, the slopes of the corresponding sides of the two triangles are equal. When the slopes of the non - hypotenuse sides of two right - triangles are equal, the angles between the sides are equal. By the AA (angle - angle) similarity criterion (the right angles are equal and the angles formed by the non - hypotenuse sides are equal), the two triangles are similar.

Answer:

The slopes of the non - hypotenuse sides of both triangles are $\frac{6}{5}$, so the triangles are similar.