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Geometry
Quiz 5-1, 5-3, 5-4 Version B
Name:___________________________
1. Matching – match the definition with the correct corresponding term.
_____1. equidistant
_____2. Angle Bisector Theorem
_____3. Perpendicular Bisector Theorem
_____4. median of a triangle
_____5. altitude of a triangle
_____6. centroid of a triangle
_____7. orthocenter of a triangle
_____8. midsegment of a triangle
a. If a point is on the bisector of an angle, then it is
equidistant from the sides of the angle.
b. Where the medians of a triangle intersect.
c. A perpendicular segment from a vertex of a triangle to
the line containing the opposite side.
d. When a point is the same distance from two or more
objects.
e. Where the altitudes of a triangle intersect.
f. A segment that joins the midpoints of two sides of a
triangle.
g. A segment whose endpoints are a vertex of a triangle
and the midpoint of the opposite side.
h. If a point is on the perpendicular bisector of a
segment, then it is equidistant from the endpoints of the
segment.
2. Find the following:
a. EF ________
b. AB ________
c. mEDF ________
3. What is the distance RQ across the pond? Explain how you know and be sure to state the theorem that
supports your explanation.
Find each measure.
4.
BC =
5.
6.
x=
DC =
7. In ∆XYZ, ZL = 48, NP = 12. Find the following.
a. ZP ________
b. PY ________
c. NY ________
8. Melissa cuts a triangle with vertices at coordinate (0, 12), (8, 1), and (16, 20). At what point should she
place the tip of a pencil to balance a triangle (what is the centroid)?
9. The vertices of ∆ABC are A(6, 10), B(2, 4), and C(8, 8). R is the midpoint of segment AB and S is the
midpoint of segment AC.
a. Find the coordinates of point R and point S.
b. Calculate the slope of segments RS and BC.
c. Calculate the length of segments RS and BC. (Hint: use the distance formula.)
d. Using slope and segment length, explain how you know that segment RS is a midsegment of
∆ABC.