Download Exam Review 3

Quarter 3 Review
Name ___________________________Hour___
Geometric Mean
1. Write a similarity statement for the three triangles. Then find x by using similar triangles.
Y
x
W
21
Z
Q
9
2. Write a similarity statement for the three
triangles.
3. Find the area of ∆WYZ.
A
D
B
C
Pythagorean Theorem
1. a)
b) Find the area of the triangle
in part a)
x
3
Remember the formula:
x
___________________________
c)
14
6
y
7
Find x. Give answer as a simplified radical.
Find y. Round answer to the tenths place.
2. Do the following triangle side lengths form a right triangle? Why or why not?
a) 8, 10, 6
b)
2,
7,3
c) 15, 11, 8
3. Which of 2(a-c) form Pythagorean triples? Explain.
P1
Special Triangles
45°
30°
Remember the patterns:
60°
45°
Find x, y, and z.
1.
a)
b)
c)
30°
60°
14
y
x
x
y
30°
9
60°
y
x
6
45°
2. a)
b)
c)
y
x
x
45°
4
y
45°
y
8
25
x
y
45°
45°
x
3. a)
b)
x
13
y
y
z
45°
60°
x
P2
10
Trigonometry – Right Triangles
Remember the trig ratios:
S ___ ___
C ___ ___
T ___ ___
12
8
sin A = _____
cos A = _____
tan A = _____
A°
10
Find x. Round sides to the tenths place and angles to the nearest degree.
1. a)
b)
c)
x
18°
32°
8
x
12
x
4
25°
7
d)
15
e)
x°
f)
26
3
x°
x°
20
12
Angles of Elevation and Depression Round to the nearest tenth.
1. The angle of elevation from a person standing on the ground to the top of a pine tree is 50°. If the
person is standing 20 feet from the tree, how tall is the tree?
P3
2. The angle of depression of a person standing at the top of a ski hill is 28° down to the chair lift at
the bottom of the hill. If the hill is 80 feet tall, how far is the chair lift from the base of the hill?
Polygons
Remember:
Sum of Interior Angles ___________________________________
Sum of Exterior Angles _____________
1. a) Find the sum of the interior angles of a regular dodecagon.
b) Find the measure of one interior angle of a regular heptagon.
c)
If an interior angle of a regular polygon is 120°, how many sides does the polygon have?
2. a)
What is the sum of the measures of the exterior angles of a regular convex decagon?
a)
If a regular convex polygon has 10 sides, what is the measure of an exterior angle?
b)
If the measure of an exterior angle of a regular convex polygon is 30°, how many sides does the
polygon have?
P4
Parallelograms Find the value of the variables.
1. a)
14
b)
65°
c)
x°
8
x
y°
y
z°
25°
v
2x + 16°
2. a)
2x°
z°
c)
y°
A
B
C
D
mAB = 1
mAC =
3. Find the area of the parallelograms.
25m
y°
3x - 10
b)
4x - 25
a)
x°
40°
5
3
w
mCD = ___
mBD = ___
10ft
b)
8m
45°
60°
6ft
4. Name the tests to prove a quadrilateral is a parallelogram. Also list which formula you would use for
that specific test if you have the coordinates of the quadrilateral.
1. Both pairs of opposite sides are __________________; formula:_____________________
2. Both pairs of opposite sides are __________________; formula:_____________________
3. Both pairs of opposite angles are __________________
4. Diagonals _____________________________; formula:____________________________
5. A pair of opposite sides is both ____________________and_________________________;
Formulas:_________________________________, ________________________________
P5
Rectangles
1. a)
9
b) A
B
c)
A
B
D
C
6
5
x°
D
20°
Find all sides and angles
C
Find all diagonal segments
AC = ____ BD = ____
2. a)
b)
3x° 3x°
c)
6x
mAB = 2
mCD = ___
mAD = ___
mCB = ___
A
B
D
C
AC = 5x + 7 BD = 8x
2
2x + 4
3. Name the tests to prove a parallelogram is a rectangle, and the formula you would use.
1.
The diagonals are ______________________; formula:___________________________
2.
All angles are ________________; (slopes of adjacent sides are ___________________)
formula: _______________________________
Rhombi
1. a)
16
b)Find x and y.
y
14
2x + 10°
4y + 2
35°
2x°
Find all sides and angles
2. Name the tests to prove a parallelogram is a rhombus, and the formula you would use.
1.
The diagonals are ______________________; formula:_________________________
2.
All sides are _______________________; formula:_____________________________
3. Find the area of the rhombi:
a)
12
b)
5
10
9
P6
Squares
1. a)
4
b)
c)
A
A
B
D
C
6
Find all angles and sides and area.
Find all angles.
Find BD and AC.
2. Name the tests to prove a parallelogram is a square.
1.
Must pass the ______________________ test
2.
Must pass the ______________________ test
Trapezoids
1.
Isosceles Trapezoids
a)
2. a)
b)
105°
x
A
B
14in
55°
40°
D
Find all angles
C
Find all angles and x.
Find AC if BD = 19
3. EF is a median.
a)
14
E
x
b)
A
F
E
x
10
D
20
B
c)
A
F
E
C
F
D
C
16
Find x
4. Find the area
B
Find ED if AE = 6
a)
14
6
10m
b)
15m
60°
27m
8
P7
Transformations – Reflections
1. Find the image of P(-3, 7)
when it’s reflected over the x-axis ______________________
when it’s reflected over the y-axis ______________________
when it’s reflected over the origin ______________________
when it’s reflected over the line y =x ______________________
2. A composition of reflections over two parallel lines is a ________________ transformation.
3. A composition of reflections over two intersecting lines is a ________________ transformation.
Transformations – Translations
1. Translate P(4, -2) according to the translation statement ( x, y)
2. Write the translation statement for the translation P (1, 9)
(x – 8, y + 1)
P’(-3, 5)
3. Write the translation statement for the graph at the right.
P
P’
A
B
Transformations – Rotations
1.
If
is
rotated
C
m
50°
with respect
to lines m and n, what is the angle of rotation?
N
2. Sketch the described rotation.
Transformations – Dilations
1. Find the image of the point P(-4, 10) with the given dilation centered at the origin.
a)
r=2
b)
r=
2. Find the length of the image of PQ with the given dilation if PQ= 8.
a)
r=5
b) r =
3. Find the preimage length if P’Q’ = 18
if r = 3
c) r =
4. Find the scale factor if PQ = 2
and P’Q’ = 10
P8