Download Math 335 — Homework 1 Solutions 1.a. A midpoint of a segment AB

Math 335 — Homework 1 Solutions
1.a. A midpoint of a segment AB is a point M on the segment AB such that AM is
congruent to MB.
b. A perpendicular bisector of a segment AB is a line CD such that
(1) the midpoint of AB lies on CD.
(2) ∠AMC is a right angle.
−→
∼ ∠DBC.
c. A ray BD bisects an angle ∠ABC if D is between A and C, and ∠ABD =
←
→
d. Points A, B, and C are collinear if C lies on the line AB.
e. Line l, m, and n are concurrent if the is a point P which lies on each of them.
2.a. Let A, B, and C be noncollinear. Then the triangle △ABC consists of all points on
at least one of the segments AB, AC, and BC.
b. The vertices of the triangle △ABC are the points A, B, and C. The sides are the
segments AB, AC, and BC. The angles are ∠ABC, ∠CAB, and ∠BCA.
c. Given a triangle △ABC, the side opposite the vertex A is the side BC. The sides
adjacent to A are AB and AC.
d. Given a triangle △ABC, the medians are the segments VM, where V is a vertex of
the triangle and M is the midpoint of the side opposite to V.
e. The altitudes of the triangle △ABC are the line segments VP, where V is a vertex
and P is a point on the side of △ABC opposite to V, such that the angle ∠VPW is right,
where W is a vertex of △ABC distinct from V.
f. An isoceles triangle is a triangle with two distinct, congruent sides. If AB and AC
are the two congruent sides, then the base is BC. The base angles are ∠ABC and ∠BCA.
g. An equilateral triangle is a triangle such that any two sides are congruent.
h. A right triangle is a triangle such that at least one of the three angles is a right
angle.