Question

determine which triangles are similar. a. 74° 81° b. 81° 24° c. 74° 25°

Explanation:

Step1: Find the third - angle of each triangle

For triangle a: Let the third - angle be $x$. Using the angle - sum property of a triangle ($x + 74^{\circ}+81^{\circ}=180^{\circ}$), we get $x = 180^{\circ}-(74^{\circ}+81^{\circ})=25^{\circ}$.
For triangle b: Let the third - angle be $y$. Using the angle - sum property of a triangle ($y + 81^{\circ}+24^{\circ}=180^{\circ}$), we get $y = 180^{\circ}-(81^{\circ}+24^{\circ})=75^{\circ}$.
For triangle c: Let the third - angle be $z$. Using the angle - sum property of a triangle ($z + 74^{\circ}+25^{\circ}=180^{\circ}$), we get $z = 180^{\circ}-(74^{\circ}+25^{\circ})=81^{\circ}$.

Step2: Compare the angles

Two triangles are similar if their corresponding angles are equal.
Triangle a has angles $74^{\circ},81^{\circ},25^{\circ}$.
Triangle b has angles $81^{\circ},24^{\circ},75^{\circ}$.
Triangle c has angles $74^{\circ},25^{\circ},81^{\circ}$.
Since triangles a and c have the same set of angles (just in a different order), they are similar.

Answer:

Triangles a and c are similar.