Answer:
a. AD and DAB are not congruent
b. point E is 1.5 from point B
c. Yes, your friend is correct
Step-by-step explanation:
(a) tan(C) = opp/adj = 3/4 so C is 36.87 or roughly 37 degrees
so A = 90 - 37 = 53
tan(DAB) = opp/adj = (4/2)/3 = 2/3 so DAB is 33.7 or roughly 34 degrees
so CAD = 53 - 34 = 19
so CAD and DAB are not congruent
(b) angle bisector is the line or line segment that divides the angle into two equal parts. It intersects BC at E so CAE = EAB = 53/2 = 26.5
so tan(26.5) = BE/3
=> BE = 3 x tan(26.5) = 3(0.499) = 1.497 or roughly 1.5
(c) a line from E perpendicular to AC will intersect AC at F, which create angle EFA or EFC a 90 degree angle
Now we have 2 right triangles AEB and AEF with the same hypotenuse which is AE and the same angles at EAF and EAB which means EB and EF are congruent
