Chapter 4.3, Problem 2WE

To determine

To complete: the proof.

Answer to Problem 2WE

Explanation of Solution

Given information:

Given:

$\overline{AM}\cong \overline{BM}$ ; $\overline{TM}\perp \overline{AB}$

Prove:

  $\overline{AT}\cong \overline{BT}$

Given figure,

Given:

  $\overline{AM}\cong \overline{BM}$

  $\Delta AMT\cong \Delta BMT$

  $\angle 1\cong \angle 2$

  $\overline{AT}\cong \overline{BT}$

  $\overline{TM}\perp \overline{AB}$

  $\overline{TM}\cong \overline{TM}$

Calculation:

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

Congruency of triangles can be proved by SSS, SAS and ASA, AAS and HL postulates.

To prove that two segments or two angles are congruent, firstly identity the two triangles in which that two segments or angles are corresponding parts. After that, prove that the identified triangles are congruent and then, state that the two parts are congruent using the reason “Corresponding parts of $\cong$ triangles are $\cong$ ”.

Given:

$\overline{AM}\cong \overline{BM}$ ; $\overline{TM}\perp \overline{AB}$

Prove:

  $\overline{AT}\cong \overline{BT}$

Appropriate statements given in the problems are as under:

  $\overline{AM}\cong \overline{BM}$

  $\overline{TM}\perp \overline{AB}$

  $\angle 1\cong \angle 2$

  $\overline{TM}\cong \overline{TM}$

  $\Delta AMT\cong \Delta BMT$

  $\overline{AT}\cong \overline{BT}$