Answered

7.) suppose they’re in a trapezoid ABC D, as in figure 12.74 AB and CD are parallel. let me be the point where the diagonals AC and BD meet. Explain why triangles AED & BEC must have the same area.(do this without measuring actual length or areas)

7 suppose theyre in a trapezoid ABC D as in figure 1274 AB and CD are parallel let me be the point where the diagonals AC and BD meet Explain why triangles AED class=


Answer :

The diagonals DB and AC are major determining factors. This is because they turn out to be transversals intercepting the two parallel lines AB and DC.

At point E, the intercepting lines DB and AC opposite angles DEA and CEB. Opposite angles are equal, therefore DEA equals CEB.

Also, since lines AC and DB intersect at point E and both terminate at parallel lines DC and AB, then the ratio of the distance from the midpoint E is the same for both diagonals. That is,

DE/EB = CE/EA

Observe that the lines opposite the equal angles DEA and CEB would also be in the same ratio as the other sides (by virtue of having equal angle measurements). That is,

CE/CB = DE/DA

That means triangles AED and BEC are similar triangles but with different measurements. The areas of both triangles must be the same.

Other Questions