Plzz solve 3,4,5,6...URGENT

Plzz solve 3,4,5,6...URGENT 3. BAD • • AE • ec • DE, 4. 't A" true BC OR' Why" S. PAR to It to PR • EFI for & A. B C Of • AEC ABC IS

Dear Student,

Solutions for the questions are as under:

Answer (3):

In the given figure, we can see that;

$$\begin{gathered} \angle BAD = \angle EAC (given in the question) \\ adding \angle DAC to both the sides, we get, \\ \angle BAD + \angle DAC = \angle EAC + \angle DAC \\ or, \\ \angle BAC = \angle EAD.....\left(i\right) (as \angle BAD + \angle DAC = \angle BAC and \angle EAC + \angle DAC = \angle EAD ) \end{gathered}$$

Hence, considering $△ABC and △ADE$

$$\begin{gathered} \angle BAC = \angle EAD \left\{From \left(i\right)\right\} \\ AC = AE \left\{Given in the question\right\} \\ AB = AD \left\{Given in the question\right\} \end{gathered}$$

Thus, based on SAS (Side Angle Side) property we can say that $△ABC and △ADE$ are congruent with each other.
Therefore, BC = DE  (the third side of the congruent triangles)


Answer (4):

It is given in the question that $△ABC and △RPQ$ are congruent with each other. Thus, the corresponding sides which are equal with each other as per the properties of congruency, will be;

$$\begin{gathered} AB = RP \\ BC = PQ \\ AC = QR \end{gathered}$$

But $BC$ will not be equal to $QR$, as these are not the corresponding sides. Thus it is false to say that $BC = QR$.

Answer (5):

It is given in the question that $△PQR and △EDF$ are congruent with each other. Thus, the corresponding sides which are equal with each other as per the properties of congruency, will be;

$$\begin{gathered} PQ = ED \\ QR = DF \\ PR = EF \end{gathered}$$

Hence, we can definitely say that $PR$ will be equal to $EF$, as these are the corresponding sides. Thus it is true to say that $PR = EF$.

Answer (6):

It is given in the question that angles A, B and C of the triangle are equal with each other. Hence we can also say that all the three angles are congruent with each other.
 
Thus,

$\angle A \cong \angle B \cong \angle C$
Now, in a triangle, sides opposite to the equal and congruent angles are always equal with each other.

Hence,

$$\begin{gathered} BC = AC (Sides correspoing to equal angles \angle A and \angle B) \\ AC = AB (Sides correspoing to equal angles \angle B and \angle C) \\ BC = AB \left(\right(Sides correspoing to equal angles \angle A and \angle C) \end{gathered}$$

Therefore, we can that $AB = BC = AC$.
Since, in $△ABC$, all the angles are equal and all the sides are equal, thus $△ABC$ is an equilateral triangle.

Hope this information will clear your doubts about the topic.

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.

Regards