Question

20 POINTS

Given square ABDF with sides 6mm in length, point C as the midpoint of side BD, and point E as the midpoint of FD (as shown in the diagram), find the measure of each of the three angles in the triangle ACE to the nearest degree and the side lengths of the triangle ACE to the nearest mm. Show your work in mathematics and explain your process in words.

Answer 1

So first thing you need to understand is that ABC and AFE are congruent triangles. This means we can find the other angles, based on ABC:

Angle FAE = 26.56505118 degrees
Angle AEF = 63.43494882 degrees

Angles ECD and DEC are both 45 degrees

Now, we can find the angles in ACE:

AEC = 71.56505118 degrees
ECA = 71.56505118 degrees
CAE = 36.86989764 degrees