Let ∆ABD, ∆BCD, and ∆ABC each be a 45-45-90 triangle, as follows:
Hi Mitch,
How did u get this to be a 45-45-90 triangle?Cant it be done without assuming this.Moreover in this case is it right that BD=1/2AC.Pl explain.
In a
must-be-true problem, the correct answer choice must be true for ANY CASE THAT SATISFIES THE GIVEN CONSTRAINTS.
The figure in the posted problem indicates the following constraint:
∆ABD, ∆BCD, and ∆ABC must all be right triangles.
I tested an easy case that satisfies this constraint.
While ∆ABD, ∆BCD, and ∆ABC do not HAVE to be 45-45-90 triangles, they all COULD be 45-45-90 triangles.
Thus, the correct answer choice must be true for the lengths shown in my post above.
Since only
B is true when BD=1, BC=√2, and AB=√2, the correct answer is
B.
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