Download MATH 514 HOMEWORK 1 In problems 1

MATH 514 HOMEWORK 1
In problems 1-4, you may only results we have already proven (e.g. SSS, ASA).
Use compass and straightedge to give constructions in problems 5-7. You should
also provide justification that your constructions do what they are required, but
you do not need to be as rigorous as on 1-4.
(1) Prove that if -A-B-C- and -B-C-D-, then -A-B-D-.
(2) Finish the proof of SSS from class for the case where the point of intersection
was outside the triangle.
(3) Prove that in an isosceles triangle, the angles opposite congruent sides are
congruent.
(4) Prove that if two angles in a triangle are congruent, the opposite sides are
congruent. (Hint: Use ASA.)
(5) Bisect a given angle using a compass and straightedge.
(6) Given a line l and a point A ∈ l, use compass-straightedge to construct a
line through A perpendicular to l.
(7) Given a line l and a point A ∈
/ l, construct (via compass-straightedge) a
line parallel to l passing through A.
For compass-straightedge constructions, you should list the steps needed to perform. For example, to construct a perpendicular bisector for the line segment AB
(as done in class), I would write something like the following:
(1) Draw circles Circle(A, |AB|) and Circle(B, |AB|).
(2) Let C and C 0 be the points where the two circles intersect.
(3) Draw the line segment CC 0 . This is the perpendicular bisector.