Question

∠dab is a right angle and ∠abc is a right angle. prove: ∠acb ≅ ∠dac. note: quadrilateral properties are not permitted in this proof. step statement 1 △abc is a right triangle ∠dab is a right angle ∠abc is a right angle try type of statement

Explanation:

Step1: Identify right - angle properties

In \(\triangle ABC\), since \(\angle ABC = 90^{\circ}\), by the definition of a right - triangle, \(\triangle ABC\) is a right - triangle. Also, \(\angle DAB=90^{\circ}\) and \(\angle ABC = 90^{\circ}\) are given as right - angles.

Step2: Use angle - sum property of a triangle

In \(\triangle ABC\), \(\angle BAC+\angle ACB = 90^{\circ}\) (because \(\angle ABC = 90^{\circ}\) and the sum of angles in a triangle \(\angle BAC+\angle ACB+\angle ABC=180^{\circ}\)). In \(\triangle DAC\) (assuming \(AD\) and \(BC\) are related in a way that \(\angle DAC+\angle BAC = 90^{\circ}\) since \(\angle DAB = 90^{\circ}\)).
Let \(\angle BAC=x\). Then \(\angle ACB = 90^{\circ}-x\) (from \(\triangle ABC\): \(\angle ACB=90^{\circ}-\angle BAC\)) and \(\angle DAC=90^{\circ}-x\) (from \(\angle DAB = 90^{\circ}\): \(\angle DAC = 90^{\circ}-\angle BAC\)).

Answer:

Since \(\angle ACB\) and \(\angle DAC\) both equal \(90^{\circ}-\angle BAC\), we can conclude that \(\angle ACB\cong\angle DAC\) (by the definition of congruent angles: angles with equal measures are congruent).