1. List the angles in order from least
to greatest.
1. Answer
•Q, R, P
2. If angle 2 = 40° and angle 3 is 110 ° ,
what is the measure of angle 1?
2. Answer
• 40 + 110 = 150
• Sum of interior angles must
equal 180 so the last angle
equals 30.
• The 30 ° and angle 1 are
supplementary so angle 1 =
150 °
3. State the theorem or postulate that
shows the s to be congruent or state N
if the s aren’t congruent. Write a
congruence statement if appropriate.
3. Answer
• QS  QS by the Reflexive
property so the two
triangles can be proven
congruent by the SSS
Theorem
4. Which point of concurrency is
represented by I?
4. Answer
•It is the incenter since
it is the intersection of
the three angle
bisectors.
5. Which measure of concurrency is
represented by O?
5. Answer
•O is the centroid since it
is the intersection of the
three medians.
6. Which measure of concurrency is
represented by H?
6. Answer
• H is the orthocenter
because it is the
intersection of the three
altitudes.
7. Which point of concurrency
completes the following sentence?
• The ______________of a
triangle is equidistant from
the vertices of the triangle.
7. Answer
•Circumcenter
8. Which point of concurrency
completes the following sentence?
•The ____________of a
triangle is equidistant
from each side of the
triangle.
8. Answer
•incenter
9. Complete the following sentence:
• The distance from a vertex of a
triangle to the centroid is ____
of the median’s entire length.
The length from the centroid to
the midpoint is ____ of the
length of the median.
9. Answer
• 2/3
• 1/3
10. What is the length MO?
10. Answer
•8
11. A rectangle has side
lengths of 12 and 20 inches.
If the perimeter of a similar
rectangle is 192, find the
length of its longest side.
11. Answer
• The perimeter of the original rectangle is
found by 12 + 12 + 20 + 20 = 64
• Then you use 192/64 to find out the scale
factor is 3.
• Apply this scale factor to 12 and 20 to get new
side lengths of 36 and 60.
• 60 is the length of the longest side.
12. Point Q is the centroid. Use the
given information to find the value of
x.
PZ  6 x  9
PQ  x  6
12. Answer
• Since PQ is 1/3 of PZ, you can
multiply PQ times 3 and set them
equal to each other.
• 3(x + 6) = 6x – 9
• 3x + 18 = 6x – 9
• 27 = 3x
• X=9
13. Point Q is the centroid. Use the
given information to find the length of
PX.
PX  4 x  7
PY  6 x  3
13. Answer
• Since a centroid is created by medians then PX
and PY are congruent. Set them equation to
each other to solve.
• 4x + 7 = 6x – 3
• 7 = 2x – 3
• 10 = 2x
• X=5
• Use the value of 5 in 4x + 7 to solve for PX
• 4(5) + 7 = 20 + 7 = 27
14.
14. Answer
• Since CDO is created by the
midpoints of MNO, each side is
half the length of MNO.
• CD = 4 so MO = 8
• CE = 8 so NO = 16
• DE = 7 so MN = 14
15. Find the value of x:
15. Answer
• Since the line X is formed by
the medians of the two sides,
it is half the length of the side
parallel to it.
• X = ½(34) = 17
16. The points A(2,4),
B(6, -2) and C(-2, 0) create
a triangle. Find the
equation of the line from C
to the median of AB.
16. Answer
• First we must find the median (midpoint) of AB.
Do this using the midpoint formula:
x = (2 + 6)/2 = 8/2 = 4
Y = (4 + -2)/2 = 2/2 = 1
So the coordinates for the median of AB is D(4,1).
• Use D(4,1) and C(-2, 0) to find the equation of the
line DC.
1 0
1

• The slope is 4  2 6
• Use the slope and a point to find b.
1 = 1/6(4) + b
1
1
1 = 2/3 + b
y  x
1 – 2/3 = b
6
3
b = 1/3
17. The point of concurrency of a
triangle that divides the medians
into a 2 to 1 ratio is called the:
a) Centroid
b) Circumcenter
c) Incenter
d) Median
e) Orthocenter
17. Answer
•centroid
18. Create a
equilateral triangle
inscribed in a circle.
18. Answer
19. Point A is the incenter of the triangle
shown. If AB is 6 meters, find the
following: AC = ?
19. Answer
AB  AC
•So AC = 6 meters
20. Five interior angles of a
hexagon have measures 100°, 110°,
120°, 130°, and 140°.
What is the measure of the sixth
angle?
20. Answer
• The sum of the interior angles of a
hexagon can be found by (n – 2) 180
with n being the number of sides.
• (6-2)180 = 4(180) = 720
• 100 + 110 + 120 + 130 + 140 = 600
• 720 – 600 = 120 so the 6th angle =
120°
21. Find the value of x:
21. Answer
• A quadrilateral has 4 sides so
(4-2)180 = 2(180) = 360
• x + x + x + 60 = 360
• 3x + 60 = 360
• 3x = 300
• X = 100
22. What is the value of m?
22. Answer
• The sum of the exterior angles of
any polygon is 360.
• m+2 + 3m + 2m + 100 = 360
• 6m + 102 = 360
• 6m = 258
• m = 43
23. What is the measure
of each interior angle of
a regular decagon (10
sided)?
23. Answer
• Use the formula (n – 2)180 to find
the sum
• (10-2)180 = 8(180) = 1440
• Since it is a REGULAR decagon all
angles are equal so divide 1440 by
10.
• Each angle measures 144°