Question

Draw triangle ABC and triangle PQR such that they are equal in area but not congruent

Answer 1

yes because see in picture

Answer 2

Triangle are equal in area but not congruent.

Step-by-step explanation:

1. Here we draw two equal length of line AB and PQ along the same line.

2. Draw a line XY which is parallel to both line AB and PQ.

3. Perpendicular distance between AB and XY is same as perpendicular distance between PQ and XY.

4. Means Altitude of both triangle $\mathbf{\Delta ABC and \Delta PQR}$ is same.

5. From here we see that

Base of $\mathbf{\Delta ABC}$ = base of $\mathbf{\Delta PQR}$

And

Altitude of $\mathbf{\Delta ABC}$ = Altitude of $\mathbf{\Delta PQR}$

6. Area of triangle is linearly depend upon base and altitude. So area of both triangle is same.

7. Here we that

  AB=PQ

  But

  BC≠ QR

 And

 CA≠RP

 So

  $\mathbf{\Delta ABC}$ is not congruent to $\mathbf{\Delta PQR}$