Question

In square abcd, the center o and the midpoint m of side ab are connected with vertices c and d. prove that the areas of amd, bmc

a. are equal
b. are different
c. sum up to the area of the square
d. depend on the side lengths of the square

Answer 1

The areas of triangles AMD and BMC in square ABCD are equal.

Step-by-step explanation:

In square ABCD, connect the center O and midpoint M of side AB with vertices C and D. The triangles AMD and BMC can be proven to be congruent (same shape and size) by the Side-Angle-Side (SAS) congruence criterion.

Therefore, since the triangles are congruent, their areas are equal. So, part (a) is correct, the areas of AMD and BMC are equal.

This conclusion is independent of the side lengths of the square.