+452 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 $ABD$.
+49 From the second sentence, we know that triangle ABC is a right isosceles triange and that B is a right angle. As BD bisects angle ABC, angle ABD is also 45 degrees, meaning triangle ABD is another right isosceles triangle. From the angle bisector theorem, we can figure out that AD=BD=6, so therefore, the area of the triangle is 6*6*1/2=18.
Feel free to tell me if I did anything wrong! :D
+49 From the second sentence, we know that triangle ABC is a right isosceles triange and that B is a right angle. As BD bisects angle ABC, angle ABD is also 45 degrees, meaning triangle ABD is another right isosceles triangle. From the angle bisector theorem, we can figure out that AD=BD=6, so therefore, the area of the triangle is 6*6*1/2=18.
Feel free to tell me if I did anything wrong! :D
