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

• by the Reflexive property so the two triangles can be proven congruent by the SSS Theorem

QS QS

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. 6 9PZ x

6PQ x

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.

4 7

6 3

PX x

PY x

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.

• The slope is

• Use the slope and a point to find b.

1 = 1/6(4) + b

1 = 2/3 + b

1 – 2/3 = b

b = 1/3

1 0 1

4 2 6

1 1

6 3y x

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

•So AC = 6 meters

AB AC

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°