Question

in triangle △abc, m∠a = 50, ab = 4.5 cm, and m∠b = 73. △abc is asa congruent with △def. find each measure. de = cm m∠f =

Explanation:

Step1: Find DE

Since \(\triangle ABC \cong \triangle DEF\) by ASA congruence, corresponding sides are equal. \(AB\) and \(DE\) are corresponding sides, so \(DE = AB\). Given \(AB = 4.5\) cm, thus \(DE = 4.5\) cm.

Step2: Find \(m\angle F\)

In a triangle, the sum of interior angles is \(180^\circ\). In \(\triangle ABC\), \(m\angle A = 50^\circ\), \(m\angle B = 73^\circ\), so \(m\angle C=180^\circ - 50^\circ - 73^\circ=57^\circ\). Since \(\triangle ABC \cong \triangle DEF\), corresponding angles are equal. \(\angle C\) and \(\angle F\) are corresponding angles, so \(m\angle F = m\angle C = 57^\circ\).

Answer:

\(DE = \boldsymbol{4.5}\) cm, \(m\angle F = \boldsymbol{57^\circ}\)