Part A:
From the appearance of the figure above, triangle A B C forms a right angle at B with A B and B C being the legs and A C being the hypothenuse.
Given that <span>A B is 20 and B C is 21, by the pythagoras theorem,
Part B:
</span>From the appearance of the figure above, triangle A B C forms a right
angle at B with A B and B C as the legs and A C as the hypothenuse.
If this is true, then the measure of angle A B C is 90 degrees.
Part C:
If A E is 10 and A F is half of A C, the special name for segment E F as it relates to triangle A B C is the midsegment.
The midsegment of a triangle is a line segment which joins the midpoints of two sides of the triangle.
Part D:
Given from part C above that line segment EF is a midsegment of triangle ABC, from the triangle midsegment theorem, line segment EF is parallel to side BC.
Thus, line BF is a transverse of parallel lines EF and BC which makes angle EFB alternate to angle FBC.
Since alternate angles are equal, given that angle <span>EFB is 43.6°, then </span>the measure of angle FBC is also <span>43.6° because they are alternate angles.
Part E:
</span><span>If Triangle DCB is congruent to triangle ABC, then angle B is congruent to angle C.
Given from part B that angle B = 90 degrees, then angle C = 90 degrees. Thus, the two adjacent angles of the quadrilateral ABCD = 90 degrees. Whih shows that the shape ABCD is a rectangle.
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