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In triangle $ABC$, point $D$ is on side $\overline{AC}$ such that line segment $\overline{BD}$ bisects $\angle ABC$.  If $\angle A = 45^\circ$, $\angle C = 45^\circ$, and $AC = 12$, then find the area of triangle $ABD$.

 Dec 30, 2023
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                                  B

 

      

          A  45                D              45   C

 

AB = CB

Angle B  = 90°

Angle ABD = 45

So angle ADB = angle CDB  = 90

So  triangles ABD and CBD are congruent  by HL

AD = CD  =  6

BD = 6

 

Area  =  (1/2)AD * BD =   (1/2) (6)(6)  = 18

 

 

cool cool cool 

 Dec 30, 2023

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