Question

in triangle vwx, vw = 4.5 inches, wx = 5.9 inches, m∠w = 28°, and m∠x = 47°. if △pqr ≅ △vwx, which statement is true?
○ qr = 4.5 cm
○ qr = 5.9 cm
○ m∠r = 28°
○ m∠r = 47°

Explanation:

Step1: Recall the property of congruent triangles

Congruent triangles have corresponding sides and angles equal.

Step2: Identify corresponding parts

Since \(\triangle PQR\cong\triangle VWX\), \(QR\) corresponds to \(WX\) (because of the order of congruence). Given \(WX = 5.9\) inches.

Step3: Check angle correspondence

\(\angle R\) corresponds to \(\angle X\). Given \(m\angle X=47^{\circ}\), so \(m\angle R = 47^{\circ}\) is wrong. \(\angle R\) does not correspond to \(\angle W\) (\(m\angle W = 28^{\circ}\)), so \(m\angle R=28^{\circ}\) is wrong. Also, units of \(QR\) should be inches (not cm as in first two options, but assuming it's a typo in options and we focus on length - \(QR = WX\)).

Answer:

\(QR = 5.9\) inches (corresponding to the option \(QR = 5.9\) cm if we consider unit as a mis - representation in problem's options)