Question

△qrs and △tuv are shown below.which statement is true?△qrs is similar to △tuv.△qrs is not similar to △tuv.there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Find angles of $\triangle QRS$

Since $\triangle QRS$ is isosceles (two sides equal), the base angles are equal. Let the base angles be $x$. Using the angle - sum property of a triangle ($x + x+72^{\circ}=180^{\circ}$), we get $2x = 180^{\circ}-72^{\circ}=108^{\circ}$, so $x = 54^{\circ}$.

Step2: Find angles of $\triangle TUV$

Since $\triangle TUV$ is isosceles (two sides equal), the base angles are equal. Let the base angles be $y$. Using the angle - sum property of a triangle ($y + y + 56^{\circ}=180^{\circ}$), we get $2y=180^{\circ}-56^{\circ}=124^{\circ}$, so $y = 62^{\circ}$.

Step3: Check similarity

For two triangles to be similar, their corresponding angles must be equal. $\triangle QRS$ has angles $72^{\circ},54^{\circ},54^{\circ}$ and $\triangle TUV$ has angles $56^{\circ},62^{\circ},62^{\circ}$. Since the angles are not equal, the triangles are not similar.

Answer:

$\triangle QRS$ is not similar to $\triangle TUV$.