Explain the teachers solution.why are those angles congruent? Is he finding t and p assuming similar triangles?how do you define the corresponding angles?
A:
There are two ways to solve this problem.
$triangle ABC$ is a right angled triangle. So, $angle BAC$ is a right angle. So, $angle BAC cong angle BDC$ (corresponding angles).
$angle BAC cong angle BDC$ (corresponding angles). So, $triangle ABC cong triangle BDC$ (Angle-Angle (AA) similarity criterion). So, $angle BAC cong angle BDC cong angle BDC$ (corresponding angles).
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