Name: ________________________
Date: __________ Period: ________
Geometry – EOC Review
Chapters 7 and 8
Chapter 7 Concepts
Important Theorems:
The altitude to the hypotenuse of a right
triangle…
 divides the triangle into two triangles that
are similar to the original triangle and to
each other.
 its length is the geometric mean of the
lengths of the segments of the hypotenuse
 separates the hypotenuse so that the
length of each leg of the triangle is the
geometric mean of the length of the
hypotenuse and the length of the segment
of the hypotenuse to the leg.
Terms
 Extended Proportion
 Extended Ratio
 Geometric Mean
 Indirect Measurement
 Proportion
 Ratio
Similar Polygons: Two polygons are similar if
corresponding angles are congruent and if the
lengths of the corresponding sides are
proportional
Side Splitter Theorem – If the line is parallel to
one side of a triangle and intersects the other two
sides, then it divides those sides proportionally.
Proving Triangles Similar : Two triangles are
similar if they have three sets of corresponding
angles congruent and three sets of corresponding
sides in proportion.
Corollary to Side Splitter Theorem – If three
parallel lines intersect two transversals, then the
segments intercepted on the transversals are
proportional.
Post or Thrm
What You Need___
AA 
two pairs of  angles
SAS
two pairs of proportional
sides and the included angles 
SSS
three pairs of proportional sides
Triangle Angle Bisector Theorem - If a ray
bisects an angle of a triangle, then it divides the
opposite side into two segments that are
proportional to the other two sides.
Solve each proportion.
1.
2
x
=
3 15
2.
3 9
=
7
x
3.
The polygons are similar. Find the values of the variables.
4.
6.
5.
7.
12
4
=
x
2x - 5
Are the following triangles similar? If so, write a similarity statement and tell whether you would use
AA, SAS, or SSS.
8.
9.
10.
11. You want to determine the height of BHS. The building casts a 6 foot shadow at the same time you
cast a 15 inch shadow. If you are 5 feet tall, how tall is the school building?
12. Refer to the figure at the right. Explain how you know that AB ED .
Find the value of each variable. Answers should be written in simplest radical form.
13.
14.
Find the value of x.
15.
16.
17.

Chapter 8 Right Triangle Relationships:

Trigonometric Ratios: SOHCAHTOA
Sin  = opposite
hypotenuse
Pythagorean Theorem
a2 + b2 = c2

Special Right Triangles
Cos  = adjacent
hypotenuse
45, 45, 90
Tan  = opposite
Adjacent
30, 60, 90

Angle of Elevation, Angle of
Depression
Find the missing length for each triangle. Answers should be written in simplest radical form.
2.
1.
x
12
5
x
20
16
3. A triangle has lengths 20, 48, and 52. What type of triangle is this? Explain.
4. A triangle has lengths 34, 35, and 60. What type of triangle is this? Explain.
Find the missing length for each special right triangle. Answers should be written in simplest radical form.
5.
6.
45°
x
4
x
30°
45°
27
Find the value of each unknown measure. Answers should be rounded to the nearest tenth.
7.
8.
8
x
9.
x
23 in
20 m
45 m
60
x
13 m
5 cm
10.
11.
12.
35
x
x
9m
x
49
10 ft.
27 m
13. While standing at the edge of the Grand Canyon, you measure an angle of depression to the
bottom of the opposite cliff of 3.6°. If you know that the walls of the Grand Canyon are 6,000
feet deep, what is the distance to the top of the opposite cliff (to the nearest thousand feet)?
14. Using an optical measuring device, a person on a ground measures a direct distance to an
airplane of 4500 meters, at an angle of elevation of 67 degrees. What is the height of the plane
above ground (to the nearest whole meter)?