Download Geometry 1 Fall Semester Review

Planes, Points, and Lines
1. Which plane is parallel to plane EFHG?
a. Name 3 coplanar points
b. Name a point collinear to point C
D
2. Name the ray that is opposite
3. If T is the midpoint of
ST = 45
S
A
U
4x + 25
4. Which point is the midpoint of
A
B
find the values of x and ST. The diagram is not to scale.
T
9x
C
B
C
–8 –7 –6 –5 –4 –3 –2 –1
?
D
0
1
E
2
3
4
5
6
7
8
5. Sketch plane PQR and plane QRS intersecting only in
?
Angles
Draw each of the following angles. Mark all properties using all relevant markings.
Acute, Obtuse, Right, Straight, Vertical Angles, Adjacent Angles, Supplementary, Complementary,
Triangle Sum Theorem, Exterior Angle of a triangle, Base/Vertex Angles of an Isosceles Triangle, Angle
Bisectors, Angle Addition Postulate, Parallel Lines with Alternate Exterior, Alternate Interior,
Corresponding, Same Side Interior.
Examples
1.
A)
C)
and
are corresponding angles.
B) 3 and 5
4 and 5
D) 3 and 7
1and 8
1
4
2
r
2
3
If r || s and m4  (6 x + 3 ) and m– 6 = (4 x + 35 )
then x  ______ .
A) 24
B) 21
C) 16
D) 15
5
6
8
3.
If r || s , then
A) 2 and 8
C) 3 and 5
and
B)
D)
s
7
are supplementary angles.
4 and 2
3 and 6
3
4.
In the figure, if m1 35 and m– 3 = 25 , then m– 4 = ____ .
1
2
4
5. The measure of the vertex angle of an isosceles triangle is 120 . The measure of a base angle
is
.
Z
6. The congruent sides of XYZare ______
X
58 °
58 °
7. Write an equation to find the value of x and find mAEB.
Y
B
A

D

3x 4
 x
E

C

8. Write an equation to find the value of x and find mAEB.
B
A

D

3x 4
E

4 x  14

C

9. If Q is in the interior of POR and mPOQ s  4 ,mQOR 2s  2 ,mPOR 26 Use
Angle Addition Postulate to write an equation, solve it for s , and find mQOR.
A
10. Find the value of x and the measures of each angle in the diagram below.
x  16
Logic
2x
Conditional Statements, Biconditional Statements, Converse, Inverse, Negation, Truth
Value, Law of Detachment, Law of Syllogism.
The sun is bright during the summer.
1.
2.
3.
4.
5.
x  20
Write as a conditional statement.
Identify the hypothesis and conclusion
Write a biconditional statement
Write the converse
Provide a counterexample
Law of Syllogism
If p  q, and q  r , then p  r
Law of Detachment
If p  q, if p is truethen q is true
Use the Law of Detachment/Law of Syllogism to draw a conclusion if possible. If not,
write No Conclusion.
6. If Jim is Texan, then he is an American. Jim is a Texan.
7. If Rachel lives in Tampa, then Rachel lives in Florida. If Rachel lives in Florida,
then Rachel lives in the United States.
C
B
Proving Triangles Congruent
Name each Postulate or Theorem used to prove two triangles are congruent. Draw a picture of two
triangles congruent by the given Postulate or Theorem.
Define CPCTC and when it is used.
Examples
1. If LMN
, then
UVW
a)
UW
b)
LMN 
c)
If 2 angles of a  are 70 and 40 , then
Mark the diagram of each problem with the given
given information. Then, give the postulate
or theorem that proves the triangles
are congruent.
2. E is the midpoint of AC and BD
3. Given: BD bisec ts ABC,BDAC
B
A
B
E
A
D
D
C
C
5. Given: BAD CDA, AB  DC
4. C is the midpoint of BD
D
A
C
A
B
C
D
E
B
B
6. Given: 1  2 , AB  AD
Prove: CB CD
A
1
C
2
D
Parallel& Perpendicular Lines including Linear
Lines that are parallel have _________ slopes.
Lines that are perpendicular have ________ ________slopes.
To write an equation of line you should use slope-intercept form____________________ or point-slope
form ______________.
Examples
1.
2.
If 4  8 ,
a) which of the lines are parallel?
b) by what theorem or postulate?
If 1 and 5
a) which of the lines are parallel?
b) by what theorem or postulate?
j
m
4
k
1
2
3
13
16
8
14
15
9
12
n
5
6
7
10
11
If m9  14  180
a) which of the lines are parallel?
b) by what theorem or postulate
4. In a plane, if l1 l2 and l3  l2 , then
3.
__________
.
(draw a sketch)
5. Given CD where C (2, 4) and D(8,12)
a) What is the slope of any line parallel to line CD?
b) What is the slope of any line perpendicular to line CD?
6.
1
Graph y  2 x  2 & y   x  4 . Are the lines parallel or perpendicular?
2
7. Write an equation in point-slope form of a line through point K(2, -1) with slope -3.
8 Given y=3x-1, write the equation of a line parallel to the given line that passes through
K(4, 5)
1
9. Given y  x  5 , write the equation of a perpendicular to the given line, that passes
3
through (1,1)
Geometry 1 Fall Semester Review
(Complete all problems on a separate sheet of paper)
Special Segments in Triangles
Draw six triangles (ABC) with each of the following segments; midsegment, angle
bisector, median, alititude, and perpendicular bisector.
G
1. If M and N are midpoints, then MN _____
N
M
H
17
K
2. If AF  FC; ABE  EBC
a)
b)
c)
d)
e)
B
G
A
D
E F
If AF  FC this means F is a __________
A median of ABC is _______
An angle bisector of ABC is ________
An altitude of ABC is _______
A perpendicular bisector of ABC is _______
C
3. Perpendicular Bisector AB intersects CD at X (Make a quick sketch)
a. Name all right angles
b. Name all congruent segment
c. State the midpoint
Can a triangle have sides with the given lengths? Explain
4. 4 m, 7 m, and 8 m
7. 1 yd, 9 yd, and 9 yd
5. 6 m, 10 m, and 17 m
8. 11 m, 12 m, and 13 m
6. 4 in., 4 in., and 4 in.
9. 18 ft, 20 ft, and 40 ft
The lengths of two sides of a triangle are given. Describe the lengths possible
for the third side.
10. 4 in., 7 in.
11. 9 cm, 17 cm
12. 5 ft, 5 ft
13. 11 m, 20 m
14. 6 km, 8 km
15. 24 in., 37 in.
Geometry 1 Fall Semester Review
(Complete all problems on a separate sheet of paper)
Proving Similarity
If quad. COLD  quad. WARM, find the perimeter of quad. WARM.
W
4
C
O
7
9
6
D
A
L
8
M
R
Find the angle measures in a triangle if they are in a ratio 3:4:5.
A 6 ft. man standing 16 ft. from a flagpole casts an 8 ft. shadow. The tip of the flagpole's shadow falls
exactly on the tip of the man's shadow.
Draw out this picture and tell me, how tall is the flagpole?
If similar write similarity statement and justify. If not similar, write NOT SIMILAR
XMW  ______________
________________________
W
X
5
4
M
12.5
10
Q
F
Solve
Solve
Solve
If similar write similarity statement and justify.
If not similar, write NOT SIMILAR
ABC  ______________
________________________
B
6
Y
4
8
A
If similar write similarity statement and justify.
If not similar, write NOT SIMILAR
TRY  ______________
________________________
L
6
9
M
10
R
C
4
T
If similar write similarity statement and justify.
If not similar, write NOT SIMILAR
TQR  ______________
________________________
2
Y
8
W
T
48
A
Q
48
C
Solve for x.
87
6
R
9
x
4
45
B
Solve for x
If GH = 20, FH = 18, EG = 8, find EF.
5
6
H
x
8
G
If DE||BC, solve for x.
E
F
A
7
x
E
Dx
5
12
C
B
If PQR  STU
TS = 8, WS = 6, QP = 32. Find VP.
P
S
Q
V
R
T
W
U
One way to show that two triangles are similar is to show that ______.
A
B
C
D
two angles of one triangle are congruent to two angles of the other
two sides of one triangle are proportional to two sides of the other
only one side of one triangle is congruent to one side of the other
only one angle of one triangle is congruent to one angle of the other
If two polygons are SIMILAR, then the corresponding sides must be _____.
A congruent
C parallel
B proportional
D similar
If
A. ay = bx
then which one of the following is not necessarily true?
B.
ax a x
 
b y b y
C.
b y

a x
D.
y x

b a
E.
yb xa

b
a