In trapezoid abcd with legs ab and cd , acad=23 dm^2. find aabd.

In the figure, ABCD is a trapezoid with legs AB and CD.

Join AC and BD.

For the triangle CAD, from the vertex C, draw an altitude CE and for the triangle ABD, from the vertex B, draw an altitude BF.

Clearly, CE = BF = h (say) --- (1)

Note that the base of the triangles CAD and ABD are the same and is AD.

It is given that ar(CAD) = .

Now, ar(ABD) =  

= from (1)

= ar(CAD)

= .

Hence, area of Δ ABD =  ..

4.6875 pounds

step-by-step explanation:

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.