Question

if m∠qrt = m∠srt = 51° and st = 45, what is qt? qt = (diagram shows points r, q, s, t with right angles at q and s, rt as a segment)

Explanation:

Step1: Identify the congruent triangles

We have \( \angle QRT=\angle SRT = 51^{\circ}\), \( \angle TQR=\angle TSR = 90^{\circ}\) (right angles), and \( RT\) is common to both triangles \( \triangle TQR\) and \( \triangle TSR\). By the Angle - Angle - Side (AAS) congruence criterion, \( \triangle TQR\cong\triangle TSR\).

Step2: Use the property of congruent triangles

In congruent triangles, corresponding sides are equal. Since \( \triangle TQR\cong\triangle TSR\), the corresponding side of \( ST\) in \( \triangle TQR\) is \( QT\). So, if \( ST = 45\), then \( QT=ST\).

Answer:

\( 45\)