Geometry Honors
Unit 9 Review
Name: _
Similar Right Triangles
1) In the figure, PA, QB, and RC are each perpendicular to AC .
a) Complete: PAC : _ and
ABQ : _
b) Which is correct:
zn
z
n
=
or
=
xm
x m+n
2) In the figure, RS is the altitude to the hypotenu
Geometry Honors
Chapter 10 Review
Name: _
Name the term that best describes the notation.
1. Duur
s
2. FH
3. C D
4. A B
5. C
6. suD
Au
r
Au
7. suB
r
8. DE
9. x = _
10. m BC = 50, B D, m E = _
A
E
A
11. In the diagram, C is the center of both circles, and
Surface Area and Volume of Solids
Solids of Revolu-on
Geometry Honors
Solids of Revolution notes
Name: _
A solid of revolution is a _ figure that is formed by
3-
dimensional
_ a two-dimensional shape around an _. The line
rota-ng
axis
UNIT 9
S imilar Right Triangles
9.1 Similar Right Triangles - notes
hyp1
D
leg1
BDC
ADB
ABC ~ _ ~ _
hyp
hyp2
alt
leg2
_ is the geometric mean between _ and _
_ is the geometric mean between _ and _
_ is the geometric mean between
UNIT 9
T he Pythagorean Theorem
Pythagorean Theorem In a right triangle, the square of the
length of the hypotenuse is equal to the sum of the squares
of the lengths of the legs.
Given: ABC is right w/ rt angle C
Prove: c2 = a2 + b2
UNIT 9
S pecial Right Triangles
45-45-90
In a 45-45-90 triangle, the hypotenuse
is _ times as long as each leg.
2
Proof:
In the triangle above, we know that c2 = a2 + a2 by the Pythagorean
theo
UNIT 9
I ntro to Trigonometry
For example, in every right triangle in which the length of the shorter leg divided by the length of the
longer leg is close to the fraction 3/5, the angle opposite the shorter leg measures close to 31. What is a
good
UNIT 9
L aw of Sines
What about a triangle that is not a right triangle?
Area = bh
h
sin A =
h
h = c sin A
c
Area = bcsinA
Likewise Area = absinC
Area = acsinB
1)
1 bc sin A 1 ab sin C 1 ac sin B
2
2
= has the job of determinin
Geometry Honors
Unit 1 Review
1)
Points A, B, C, and D are coplanar. A, B, and C are collinear, but B, C, and D are not.
How many different lines are determined by points A, B, C, and D?
a) 3
2)
d) can not be determined
b) exactly 1
c) infinitely many
d)
Constructions Activity #5
Perpendicular Lines
Name:
Date:
Use the following steps to construct a line that passes through a given point P and is
perpendicular to a given line l.
1. Place
Geometry (Honors)
Unit 3 Perpendicular & Parallel Lines
Problem Packet
Complete all work on a separate sheet of paper.
1. 1 and 2 are supplementary.
a. m1 = 2y
m2 = 3y 15
m2 = _
2. 1 and 2 are complementary,
Find the value of x.
b. m1 = 5m2
m 2 = x
m1 = _
Geometry Honors
Chapter 3 Review
Name: _
Use the diagram at the right to answer #1-3.
1) Name all segments parallel to AE .
2) Name all planes intersecting plane BCN.
3) Name all segments skew to DC .
Identify each pair of angles as alternate interior/ext
Geometry (Honors)
Unit 4 Polygons
Problem Packet
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32. What is the sum of the measures of the interior angles of a dodecagon?
33. How many sid
Geometry Honors
Unit 4 Review
Name: _
1) Find the values of x and y.
2) Find the measure of 1 . 3) List the sides in order from
longest to shortest.
4) Solve for the variables.
5) Solve for x.
6) Solve for x.
7) Find the value of y.
8) Find the value of e
Geometry (Honors)
Unit 5 Transformations
Problem Packet
Use the diagram at the right to complete the statement.
9.
11.
AB _
_ BFG
10.
D _
12.
B _
13. figure ABED figure _
Use the diagram at the right to name the image of 1 after each reflection.
14. refle
Geometry
Reflections - Examples
Name: _
Use the diagram at the right to name the image of the figure after the reflection.
1)
reflection of B in HD
2)
reflection of G in HF
3)
reflection of JOD in BF
4)
reflection of BCD in BD
5)
reflection of LKF in QF
G
Geometry Honors
Unit 5 Review
1)
Name: _
Reflect the given point over each line.
Give the coordinates of the image.
y
a)
A _
b)
B(5, -1) over y = -x
B _
c)
C(-4, 5) over the line y = 3
C _
d)
D(-2, 3) over the x-axis
D _
e)
2)
A(0, -2) over the y-axis
E(1
Geometry (Honors)
Unit 6 Proof with Congruent Triangles
Problem Packet
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12. For each of the pairs of triangles below, name the congruence postulate (if any) that
will prove the triangles congruent. If the triangles can be
Unit 6
Proving Triangles Congruent
More Than One Pair of Congruent
Triangles
Notesheet #8 - More Than One Pair of Congruent Triangles
Sometimes you need to use corresponding parts of one pair of congruent triangles to help you prove a second pair
of cong
Unit 6
Proving Triangles Congruent
Isosceles Triangles and Overlapping
Triangles
Given: PR ST
These two results do not use congruent triangles. However, they can still be used
NP VT
in proofs. They may appear either before or after the 3-to-1 connector.
*
Similar Polygons
A proportion is an equation that equates two _.
ratios
A proportion is an equation that equates two _.
Solve each of the following proportions.
Solve each of the following proportions.
6
15
15=
1) 6
1)
x=2 7
+
x+2 7
15x + 30 = 42
1 5 x
*
Proving Triangles Similar
_
AA
1)
If _ of one triangle are
two angles
_ to _ of
two angles
another triangle, then the triangles are
similar.
_
SSS
2)
AB BC CA
=
=
PQ QR RP
the lengths
If _ of the corresponding
_sides _ of two triangles are _
_
_proporti
*
Dilations
Worksheet #1
b) Describe how the image (ABC) compares to the preimage (ABC):
1. b) Describe how the image (ABC) compares to the preimage (ABC):
in size
in size
in shape
in shape
c) Where is the image (ABC) located in relation to ABC and po
Geometry Honors
Unit 8 Review
Name: _
1) For each pair of triangles indicate whether the two triangles are similar. If so, state the theorem or
postulate that can be used to prove the triangles similar.
2) a) What must be the length of MD for the triangle