Chapter 4.1, Problem 1MRE

To determine

To write: the proof of $\angle 1\cong \angle 2$ in two column form.

Explanation of Solution

Given information:

Given: $\overline{AD}\perp \overline{BC};\overline{BA}\perp \overline{AC}$

  

Calculation:

The two triangles are said to be congruent if they are copies of each other and if their vertices are superposed, then can say that the corresponding angles and the sides of the triangles are congruent.

  

Given: $\overline{AD}\perp \overline{BC};\overline{BA}\perp \overline{AC}$

Prove: $\angle 1\cong \angle 2$

Proof:

Statements	Reasons
1. $\overline{AD}\perp \overline{BC};\overline{BA}\perp \overline{AC}$ 2. $\angle BAC$ and $\angle BDA$ are right angles 3. $\Delta BAC$ and $\Delta BDA$ are right triangles 4. $\angle 1$ and $\angle B$ are complementary angles; $\angle 2$ and $\angle B$ are complementary angles 5. $\angle 1\cong \angle 2$	1. Given. 2. Definition of $\perp$lines. 3. Definition of right triangles. 4. The acute angles of a right triangle are complementary. 5. If two angles are complementary of the same angle, then the two angles are congruent.