Question

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

Explanation:

Step1: Calculate the third angle of \(\triangle RST\)

The sum of angles in a triangle is \(180^{\circ}\). For \(\triangle RST\), let the third angle be \(\angle S\). Then \(\angle S=180^{\circ}-(55^{\circ} + 45^{\circ})=80^{\circ}\)

Step2: Calculate the third angle of \(\triangle UVW\)

For \(\triangle UVW\), let the third angle be \(\angle W\). Then \(\angle W=180^{\circ}-(55^{\circ}+75^{\circ}) = 50^{\circ}\)

Step3: Check the similarity condition

Two triangles are similar if their corresponding angles are equal. Since the angles of \(\triangle RST(55^{\circ},45^{\circ},80^{\circ})\) and \(\triangle UVW(55^{\circ},75^{\circ},50^{\circ})\) are not equal.

Answer:

\(\triangle RST\) is not similar to \(\triangle UVW\)