posted by Annie

given isosceles triangle ABC, line AB = BC, and BD is the angle bisector of isosceles triangle ABC

prove AB x DC = BC x AD

Aren't the two halves congruent? (SAS)

If so, then DC is equal to AD.

Don't the ratios AB:AD=BC:DC by corresponding parts?

how do i write that out like on a table though like step by step

I won't do the table otherwise that defeats the purpose of the assignment. If you do the exercise and post your work for evaluation that's fine. We'll comment on it.
Start by drawing a diagram and labeling the parts. Then see what the given statement corresponds to in terms of the triangles parts. Be sure to check the book for theorems to use and examples to follow.

ok i wrote it all out but then when the last thing is AB X DC = BC X AD i don't remember what to write as the reason

If you proved that the triangles are congruent by some method such as SAS, then AB:BC=DC:AD i.e. corresponding parts are in the same ratio, and
because the product of the means = the product of the extremes, and the commutative property of multiplication.
I think that's sufficient, but check your text too. Hopefully I didn't use something not available to you here.

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