This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify the given information. We are given two triangles, PQR and STU. We are also given that two pairs of corresponding angles are equal: P = S Q = T Step 2: Prove the similarity of the triangles. If two angles of one triangle are equal to two angles of another triangle, then the third angles must also be equal (since the sum of angles in a triangle is 180^). This means the triangles are similar. In PQR and STU: 1. P = S (Given) 2. Q = T (Given) 3. R = U (Sum of angles in a triangle) Therefore, PQR STU (Angle-Angle-Angle similarity criterion). Step 3: State the proportionality of corresponding sides. When two triangles are similar, the ratio of their corresponding sides is equal. The corresponding sides are: • PQ corresponds to ST (opposite R and U) • PR corresponds to SU (opposite Q and T) • QR corresponds to TU (opposite P and S) So, we can write the ratios of corresponding sides: (PQ)/(ST) = (PR)/(SU) = (QR)/(TU) Step 4: Conclude the required statement. From the proportionality of corresponding sides, we can directly state the required theorem: (PQ)/(ST) = (PR)/(SU) That's 2 down. 3 left today — send the next one.