Prospect Hill Academy
Geometry Midterm Review
Heyl/Sparkes/Pfrommer
Like all your midterms, your geometry midterm is worth 20% of your first semester grade. (10% of
your year grade)
Your midterm is broken into three sections as follows:
Section 1
Section 2
Section 3
Section 4
Short Answer
Vocabulary/Notation
Multiple Choice
Free Response
~25 questions
~20 questions
~5 questions
~5 questions
4 or 2 points each
2 points each
2 points each
4 points each
~50%
~25%
~5%
~20%
Steps for studying:

Organize materials- find old tests, quizzes, notes, portfolios.

Review vocabulary—look up and make a list of any terms that you could not
describe/identify/sketch.

Look at skills list and identify places where you may be weak. Look through your notes, then
work on some problems from those sections. Write down example problems and important
theorems so you can look back at these later.

Be awake, engaged, ask questions, answer questions, and be an active group/class member
during in class reviews

Work on problems from this review packet .

Look back over old quizzes and portfolios, rework some of those problems.

Night before- look over your written review materials, including the vocabulary list you created
and the example problems you wrote.

Sleep and eat breakfast!
Topics on Midterm Exam
Chapter 1
 geometry vocabulary and notation
 draw and label a figure using correct notation given a written explanation using symbols
 Write a description of a geometric figure using correct notation and vocabulary.
Chapter 2: Reasoning in Geometry
 vertical angle conjecture, linear pair conjecture and properties of parallel lines and angles
(alternate interior/exterior angles, corresponding angles)
𝑦 −𝑦
 Find the slope of a line with 2 pts. 𝑥2−𝑥1


2
1
find the slope of a line on a graph
find the slope of a parallel or perpendicular line given the slope of a parallel or perpendicular
line
Chapter 3: Triangle Properties
 triangle sum conjecture- all the angles in a triangle add up to 180
 Draw, label, and define the median and midsegment of a triangle.
 Solve problem using the definition of a midsegment, median, perpendicular bisector.
 Apply the Side-Angle Inequality Conjecture to determine the order of angles or sides from
least to greatest.
 isosceles triangle conjecture-base angles are congruent
 triangle inequality conjecture- Determine if any set of three given sides will make a possible
triangle.
 congruent triangle shortcuts: SSS, SAS, AAS, ASA
 CPCTC/Proofs
Chapter 5: Polygon Properties
 interior angle sum of a polygon, interior angles of regular polygons
 exterior angle sum of a polygon, exterior angles of regular polygons
 Given a description or a labeled picture, identify the most specific name of the figure (i.e.
square, rectangle, rhombus, and parallel).
 Given a shape, name what other quadrilateral categories it satisfies.
 Describe the relationship between squares/rectangles/rhombus/parallelograms
 Know all the properties/conjectures of trapezoids, kites, parallelograms, squares, rectangles,
rhombuses to solve problems for missing sides, angles, and sides and angles of the
diagonals of the quadrilateral
 Accurately label diagrams of kites, trapezoids, parallelograms with all their parts
 Find the length of a midsegment given the bases, or find a missing base given a midsegment
and one base of a triangle or trapezoid
Chapter 6: Circle Properties
 Draw and identify the parts of a circle (chord, radius, tangent, diameter, minor arc, major arc,
semicircle, secant, central angle)
 Find missing arc lengths, chord lengths, and angle measurements using the chord properties
and conjectures
 Use the properties of tangents to solve for missing angles and lines in circle diagrams
 Apply the properties of inscribed/central angles to find missing angles and arc measures in a
given problem
Practice Problems-UNIT 1
1. Match each term with one of the items below.
II. Draw and label a diagram with the given information:
̅̅̅̅ with midpoint M.
13. A line segment 𝐴𝐵
̅̅̅̅ and 𝐸𝐹
̅̅̅̅ ≅ 𝐸𝐹
̅̅̅̅ so that 𝐴𝐵
̅̅̅̅
15. Draw 𝐴𝐵
14. Draw < 𝐵𝐴𝐾
̅̅̅̅ and 𝐾𝐹
̅̅̅̅ so that 𝐷𝐿
̅̅̅̅
16. Draw 𝐷𝐿
̅̅̅̅
𝐾𝐹
17. Draw < 𝐴𝐵𝐶 that is 125º
18. Draw < 𝑋𝑌𝑍 that is 20 º
19. Draw a plane that contains 4 points A, B, C, and D, with no more than 2 collinear points.
20. Draw an angle < 𝐸𝐹𝐺. Now draw ray ⃗⃗⃗⃗⃗
𝐹𝑃 as its angle bisector. Name and find the measure
of all 3 angles.
III. Short Answer Questions:
21. What is the difference between a segment and a ray?
22. What point would be the vertex in < BCS and how do you know ?
23. Draw a shape that is a polygon, and one that is NOT a polygon, and tell me why.
Polygon
Not a polygon
24. Draw a polygon that is convex, and one that is concave, and tell me why.
Concave
Convex
25. Draw a regular polygon, and explain why it is regular.
26. Draw and label an isosceles acute triangle CAT where AC ≅ CT
27. Draw circle J, with tangent lines AP and GW where AP ll GW.
28. What is a conjecture?
Use your definitions/vocab sheet to draw a picture for each of these examples, and then accurately LABEL all
important information
A square LMNO
Angle NAT= 110° with bisector ⃗⃗⃗⃗⃗
𝐴𝑆
Line segment
⃡⃗⃗⃗⃗
𝐵𝐴 where
̅̅̅̅̅
𝑀𝑅 with a perpendicular bisector
̅̅̅̅̅
𝑀𝑅 = 19 ft
A regular pentagon LABEL with diagonals
LB and LE
Parallelogram DOGS with DO ≅ GS
Right triangle GEO with
G and E = 45°. Side GO = 30 ft
Circle with diameter̅̅̅̅
𝑆𝐿, = 40 in
and has tangents ⃗⃗⃗⃗⃗
𝐴𝐵 and ⃗⃗⃗⃗⃗
𝐶𝐷 where
⃗⃗⃗⃗⃗
⃗⃗⃗⃗⃗
𝐴𝐵 ll 𝐶𝐷
Triangles ABC and DEF where
ABC ≅ DEF by SAS
Two triangles CAT and DOG where
CAT ≅ DOG by AAS
Unit 2
1. Determine the measure of each lettered angle.
2. Determine the measure of each lettered angle.
Two triangles MAN and BOY where
MAN ≅ BOY by ASA
3. Triangle XYZ and two angle measures are shown in the diagram below. (multiple choice)
What is the measure of
Y?
A. 50°
B. 85°
C. 90°
D. 95°
4. The lines in the diagram below represent four streets in Linda's hometown. (multiple choice)
Keller Street is parallel to Garcia Street, and Main Street is parallel to Second Street.
If m
1 = 95°, what is m
A.
75°
B.
85°
C.
95°
2?
D. 105°
5. What is the slope of a line perpendicular to y = 3x + 6.7
6. What is the slope of a line parallel to y = 3x + 6.7
7. Find the slope of the line passing through (9, 5) and (-3, 1).
8. Line j is represented by the equation below.
line j: y = 2x + 4
a. What is the slope of line j? Show or explain how you got your answer.
b. What is the slope of any line that is parallel to line j? Explain your reasoning.
c. Write an equation for the line, k, that is parallel to line j and passes through the point
with coordinates (3, 7). Show or explain how you got your answer.
d. Write an equation for the line, h, that is perpendicular to line j and passes through
the point with coordinates (8, 10). Show or explain how you got your answer.
9. In the diagram below,
.
Based on the angle measures in the diagram, what is the value of y?
A. 75
B. 90
C. 95
D. 120
10. The coordinate grid below shows point H(5, 2), point K(7, 10), and
What is the slope of
.
? (Multiple Choice)
A.
B.
C.
D.
11.
10. In the diagram below,
intersects
at point G.
Based on the angle measures in the diagram, what is the value of x?
A. 34
B. 38
C. 43
D. 56
11. Each of the two interior supports for part of a roof is perpendicular to a rafter, as shown below.
What is x, the measure, in degrees, of the angle formed by the two interior supports?
A. 50
B. 65
C. 90
D. 130
12. In the figure shown below,
What is the measure of
is parallel to
, and
intersects
at Q.
?
13. In the diagram below, lines k, m, and n are parallel lines intersected by line p.
Line p is not perpendicular to lines k, m, and n.
Which of the following angles has a measure that is not equal to the measure of
A.
2
B.
3
C.
4
D.
5
1 ? (multiple choice)
Unit 3
Use the information given to complete each statement. If the triangles are congruent, complete the
statement and state the shortcut used. If the triangles are not congruent, state that they are not
congruent.
a.
c.
d.
b.
2.
3. The diagram below shows




is an isosceles triangle with congruent sides
Point M lies on
, and point N lies on
is parallel to
The length of
.
.
.
is 23 feet, and the length of
a. What is the length of
b. What is
and
is 10 feet.
? Show or explain how you got your answer.
? Show or explain how you got your answer.
c. What is
? Show or explain how you got your answer.
4.Are these triangles?? If not, draw or explain why it doesn’t work
19 cm, 33 cm, 48 cm
37 n., 65 in., 92 in
13 Km, 21 Km, 32 Km
17.1 ft, 21.4 ft, 34.8 ft
5.If you have a triangle with sides 24 and 41, what is the smallest possible third side, and what is the
greatest possible third side?
The biggest possible side is ___________________________
The smallest possible side is___________________________
h
6. Arrange these sides or angles from smallest to greatest:
23
10
54
a
19
f
d
c
j
g
84
12
42
17
14
e
b
7. III. Find the missing labeled angle or angles:
y
73°
51°
68°
8. Solve for x and y
x
125°
9. Solve for x
10.
12. Arrange the unknown letters from greatest to least.
13.
14. Arrange the unknown letters from greatest to least.
15.
16. Could you construct a triangle with lengths 23cm, 27cm and 50cm? Why or why not?
N
Diagram:
G is the midpoint of NH and TU
T
G
U
Prove that NT  HU
Statements
Reasons
H
T
̅̅̅̅ ≅ 𝑇𝑃
̅̅̅̅
Given: Kite TARP with 𝑇𝐴
̅̅̅̅
𝑇𝑅 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 < 𝑇
A
P
Prove: < 𝐴 ≅ < 𝑃
Reasons
Statements
R
UNIT 4
1. Find all the lettered angles:
2. Find all the lettered angles:
3.
4. Find all the lettered angles
76°
81
°
Section 2: A few short answer questions
5. How many degrees are there in a 15 sided polygon? ____________
6. How do you find out how many degrees are in a polygon? (What is the formula)
7. The exterior angles of a polygon always add up to _____________.
8. If you have a regular hexagon, how many degrees is each of the interior angles?
9. If you have a regular decagon, each of the exterior angles is ________________.
10. If the measure of one exterior angle of a polygon is 15°, how many sides does the polygon have?
11. What is a kite? (Draw and label one)
12. What do you know about the non-vertex angles of a kite?
13. What do you know about the diagonals of a kite?
14. What is a trapezoid? (Draw and label one)
15. What do you know about the two angles on the left or right side of a trapezoid?
16. What is an isosceles trapezoid? (Draw and label one)
17. What do you know about each pair of base angles in an isosceles trapezoid?
18. What is a midsegment?
19. Draw a triangle with a midsegment drawn and labeled.
20. What do you know about the length of a midsegment of a triangle?
21. Draw a trapezoid with a midsegment drawn and labeled.
22. What do you know about the length of the midsegment of a trapezoid?
23. The following two problems are kites, find the missing angles or sides:
24. The following two problems are isosceles trapezoids, find the missing angles or sides:
25.
26.
27.
4)
3)
30
29.
31.
32.
33,
34.ABCD is a parallelogram
35. ABCD is a parallelogram
36.
37.
38.
UNIT 5
1. Find the perimeter
2.
3.
4.
6.
5.
7.
10.
12. Determine the measures of the arcs.
13.
14.
Review Problems
If you want some other problems to go back and try…
chapter page
1
37
2
109
122
129
134
3
167
4
212
201
206
216
223
231
5
257
262
269
281
6
310
315
322
333
343
Problems
1-4
1-3
1-5
1-7
1-3
1-4
6-8, 11
2, 8,9
1-7
1-4, 12
9-14
1-9
1-10
4-6
1-6
1-3
1
3
1-3
1-6
1-4