SOLUTION: Given: Quad ABCD is a trapezoid Prove: A(Triangle ACD) = A(Triangle BCD) Statements: Reasons:

Question 966259: Given: Quad ABCD is a trapezoid
Prove: A(Triangle ACD) = A(Triangle BCD)
Statements:

Reasons:
Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!

Let ABCD be a trapezoid with the bases AB and DC, and AC and BD be its diagonals.
(Figure 1). We need to prove that the triangles ACD and BCD have equal areas.

Let us draw the altitudes AE and BF in the trapezoid ABCD from vertices A and B
to the base DC (Figure 1).
Notice that these altitudes are congruent as the opposite sides of the rectangular ABFE.

Now, the triangles ACD and BCD share the common base DC and have
congruent altitudes to the base. Therefore, these triangles have the same area.

Figure 1

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