Download File - Math Planets

Review Booklet
SIMILARITY,
CONGRUENCE, AND
PROOFS
5 Ways to Prove Triangles
Congruent
1. SSS: All 3 sides are exactly the same
2. SAS: 2 congruent sides and the angle
in between
3. ASA: 2 congruent angles are the side
in between
4. AAS: 2 congruent angles and a side
NOT in between
5. HL: ONLY FOR RIGHT TRIANGLES –
Hypotenuse and 1 Leg
CONGRUENCE STATEMENT
Order matters!
Match up corresponding parts.
Example: ABC  DEF
Triangle Sum Theorem
The 3 angles in a triangle add
180
up and equal ______.
Exterior Angle Theorem
The 2 remote interior angles add up and
equal the exterior angle
Remote
Angle
Exterior
Angle
Remote
Angle
Isosceles Triangle
• 2 congruent sides
• Opposite of the congruent sides
are congruent angles
Rigid Motion – the shape will still
be congruent after the move
1. Reflection
2. Translation
3. Rotation
Dilate the figure by 1/2. Use the origin as the
center of dilation.
A  4,4  
A '  2,2 
B  2, 6  
B '  1, 3 
C  6,0  
C '  3,0 
Find the center of dilation
Center
 2,2 
Similar Polygons
1. Corresponding angles are
congruent
2. Corresponding sides are
proportional
3. Similarity Statement
ABC ~ DEF
Solve for x and y.
ABC ~ SLT
L
A
10
cm
B
x
24 cm
x = 26 cm
y
5 cm
S
13 cm
C
T
y = 12 cm
In similar triangles, angles are congruent
and sides are proportional
ABC ~ SLT
Find the missing angle measures.
A
L
53
S
B
C
37
T
mC  37 mL  90
mS  53
Find the perimeter of the smaller
triangle.
12 cm
Perimeter = 60 cm
4 cm
Perimeter = x
x = 20 cm
3 ways to Prove Triangles Similar
1)Angle-Angle (AA~) Similarity
Postulate
2)Side-Side-Side (SSS~) Similarity
Theroem
3)Side-Angle-Side (SAS~) Similarity
Thm
Determine whether the triangles are similar. If so,
tell which similarity test is used and complete the
statement.
68°
43°
68°
43°
V
Y
7
W
11
3
U
X
5
Z
Prove that RST ~ PSQ
1. Two sides are proportional
SAS~2. Included angle is congruent
S
4
P
12
R
5
16 20

4
5
4 4

1 1
Q
15
T
S  S
reflexive
A tree cast a shadow 18 feet long. At the
same time a person who is 6 feet tall cast a
shadow 4 feet long. How tall is the tree?
tree's shadow
tree's height

person's shadow person's height
18 x

4 6
x  27
Review Booklet
Right Triangle
The Pythagorean Theorem
“For any right
triangle, the sum of
the areas of the two
small squares is
equal to the area of
the larger.”
a 2 + b 2 = c2
Ladder Problem
Solution
a2 + b2 = c2
72 + b2 = 252
49 + b2 = 625
b2 = 576
b = 24 m
How did you do?
A=7m
Trig Ratios
Trig Ratio
What is cos R?
What is sin R?
What is tan R?
21
29
20
29
20
21
Co-Function Relationships
sin   cos(90  )
cos   sin(90  )
1
tan  
tan(90  )
Co-Function Relationships
26
Cos 64 = Sin ____
Find a Missing Side
Solve for x. Round to the nearest tenth.
x = 17.6
x
Find a Missing Angle
Solve for . Round to the nearest tenth.

 = 31.4
The angle of elevation from a ship to the
top of a 35 meter lighthouse on the coast
measures 26. How far from the coast is the
ship? Round to the nearest tenth.
tan 26 = 35/x
x = 71.8 m