Download Midpoint Formula: Distance/Length Formula: Mark and label the

Name: ____________________________________
Date: ____________
Period: _____
Geometry w/ Trig
REVIEW PART 1
for Unit 1 Foundations Test
1) In the figure at the right, QP and QR are opposite rays. QS bisects PQT.
If mPQT = 60° and mPQS = (4x + 14)°, find the value of x.
Mark and label the diagram first!
Reason: If a ray _________________ an angle, then ___________________________________________________.
2) a) Look in your notes for the Distance Formula and the Midpoint Formula.
b) Take a few minutes to study and memorize the two formulas.
c) When you feel ready, test yourself by writing the formulas in each box below from memory.
d) Check your answer. How did you do? Correct any mistakes made. Then apply the formulas in part (e) below.
Distance/Length Formula:
Midpoint Formula:
3) Use the given information below to complete steps (a) – (c) below.
Given: RS = 2x,
ST = 5x + 4,
RT = 32
a) Draw and label a diagram where S is between R and T.
b) Set up an algebraic equation and find the value of x. Then find RS and ST. Circle your answers.
c) Check off the definition or postulate that you applied to set up your equation above.
If a point is the midpoint of a segment, then it divides the segment into 2 congruent segments.
If 2 lines are perpendicular, then they intersect to form a right angle.
Segment Addition Postulate
4) Use the diagram at the right to answer the following questions.
a) If x = 5, then does AB bisect CAD? Explain your reasoning.
b) If x = 8, then does AB bisect CAD? Explain your reasoning.
5) Refer to the figure at the right.
a) Name a pair of opposite rays: ____________ and ____________
b) Name two acute vertical angles: ____________ and ____________
c) Name an angle that forms a linear pair with AEC: ____________
d) Name the intersection of GH and plane Q: ____________
e) Name the intersection of all 3 lines in the diagram: ______________
f) Is E the midpoint of AB ? Explain why or why not.
6) Refer to the figure at the right.
a) Name the vertex of 4. _____________
b) Name the sides of BDC. _____________
c) Write another name for DBC. _____________
7) Find each of the angle measures below. Then give an explanation that supports your reasoning.
a) mSTE = _____________
Explain: __________________________________________________
__________________________________________________
b) mLTE = _____________
Explain: _____________________________________________________________________________________
c) Given that TN bisects LTE, then mNTE = _____________
Explain: _____________________________________________________________________________________
REVIEW PART 2
for Unit 1 Foundations Test
DIRECTIONS:
Diagram
Diagram
Try your best to complete this without using your notes! 
First, sketch a diagram that represents the given statement. If possible, show markings too!
Then, match the hypothesis (numbers) with the appropriate conclusion (letters).
Definitions/Theorems (Conditional Statements)
1. If a point is a midpoint of a segment, then _______
A. they form a right angle.
2. If two angles form a linear pair, then _______
B. their angle measures have a
sum of 180 degrees.
3. If two angles form a right angle, then _______
C. they are supplementary.
4. If two lines are perpendicular, then _______
D. they are complementary.
5. If two angles are complementary, then _______
E. it divides the segment into
two congruent segments.
6. If two angles are supplementary, then _______
F. their angle measures have a
sum of 90 degrees.
Definitions/Theorems (Conditional Statements)
7. If two angles are vertical angles, then _______
G. it measures 90 degrees.
8. If two angles are congruent, then _______
H. they are congruent.
9. If segments are congruent, then _______
I. it divides the segment into
two congruent segments.
10. If an angle is a right angle, then _______
J. it divides the angle into two
congruent angles.
11. If a line bisects a segment, then _______
K. their lengths are equal.
12. If a ray bisects an angle, then _______
L. their measures are equal.
For Exercises 13-16, use the triangle on the graph to the right.
Q
13. Find the coordinates of the midpoint of PQ . Show all work.
R
P
14. To find the lengths of sides PR and QR of ΔPQR,
you do NOT need the Distance Formula. Explain why not:
_______________________________________________________________________________________________
Now, find the 2 side lengths: PR = ________ units and QR = ________ units
15. Find the length of the third side PQ . SHOW ALL WORK, including the formula as your first step.
(Remember, the formula must be memorized for your test!)
16. Are any of the sides of ΔPQR congruent? Explain. ____________________________________________________
For Exercises 17-19, use the figure at the right. (Multiple-Choice)
17. Which pair of angles are vertical angles?
A)  RST,  TSU
B)  TSU,  USV
C)  RSX,  TSU
D)  RSX,  XSW
(10y + 10)°
18. Which angle is supplementary to  USV?
A)  TSU
B)  VSW
C)  RSV
T
S
R
D)  WSR
5x°
4x°
X
W
V
19. Find the values of x and y.
A) x = 10, y = 12
B) x = 20, y = 7
C) x = 10, y = 8
D) x = 50, y = 40
U
20. Find the value of x.
21. Mark the diagram and find the value of x.
Reason: If two angles _____________________________,
Reason: If two angles _____________________________,
then __________________________________________.
then __________________________________________.
22. Mark the diagram and find the value of x.
23. Given: KL  KM , mark the diagram and find the
value of x.
Reason: If two angles _____________________________,
Reason: If two rays _____________________________,
then __________________________________________.
then __________________________________________.
24. Use the graph of the segment to plot a point C that would create two new segments with the given ratio.
a) Given: a ratio of 1:2
b) Given: a ratio of 2:3