Download Name:__________________________________________________________ Date:_______________________ Period:__________

Name:__________________________________________________________
Similar Triangles Review Sheet
Date:_______________________ Period:__________
Geometry Honors
Directions: Answer the following questions completely. Please remember to show all work that is necessary for the
test.
Ratio of Similitude:
1) The sides of a triangle are 5, 6, and 10. Find the longest side of the triangle, if the shortest side is 15.
2) Two triangles are similar. The lengths of the sides of the smaller triangle are 4, 6, 7. The shortest side of the
larger triangle is 16. What is the length of the largest side?
3) A boy looks into a mirror that has been placed on the ground 3 meters away and sees the reflection of the top of
a telephone pole. If the mirror is 21 meters away from the telephone pole and the person is 2 meters tall, how tall
is the telephone pole?
4) The sides of a quadrilateral measure 12, 15, 24, and 18. If the shortest side of a similar quadrilateral measures 4,
find the measures of the remaining sides of this quadrilateral.
5) In the accompanying diagram,
length of
6)
and
(a) 8.3 inches
inches,
(b)
is similar to
inches
and
, and
(c)
inches
. What is the
. What is the length of DE?
(d) 39 inches
7) Henry casts a shadow, 3 feet in length. His son who is 3.5 feet tall, casts a shadow that is 1.8 feet in length.
Which of the following best represents Henry’s height?
(a) 5 ft 6 in
(c) 5 ft 8 in
(c) 5 ft 10 in
(d) 6 ft
8)
. Find the perimeter of
Overlapping Triangles:
1) Find the value of x.
2) Find the length of FJ.
3) Find the value of n.
4) Find the value of x.
5) Find the value of the height (h) in the following diagram at which the tennis ball must be hit so that it will just
pass over the net and land 6 meters away from the base of the net.
Midsegment:
1) In the diagram below, the vertices of ΔDEF are the midpoints of the sides of equilateral triangle ABC, and the
perimeter ΔABC is 36 cm.
What is the length, in centimeters of EF?
(1) 6
(2) 12
(3) 18
(4) 4
2) In the diagram below of ΔACT, D is the midpoint of AC, O is the midpoint of AT, and G is the midpoint of CT.
If AC = 10, AT = 18, and CT = 22, what is the perimeter of parallelogram CDOG?
(1) 21
(2) 25
(3) 32
(4) 40
3) MT is a midsegment of
. Use the diagram to the right to answer the following questions.
(a) What is the measure of
?
(b) What is the measure of
?
(c) What is the measure of
(d) What is the measure of
?
4) A student makes the rabbit shadow that you see in the diagram. The part of his hand making the shadow is 4.5
inches tall, and it is halfway between the flashlight and the wall. The top of his fingers are halfway between the
flashlight and the top of the shadow.
(a) How tall is the rabbit?
(b) Now assume that the boy’s hand is 3.7 inches and the
shadow is 7.6 inches. Is the part of the boy that creates the
shadow a midsegment?
5) X, Y, and Z are midpoints of the sides of triangle ABC. XY is
6) Given
, and
. How long is
construct midsegment XY, if the midpoint of AB is X and the midpoint of AC is Y.
[Leave all construction marks.]
Ratio of Similarity:
1) If the ratio of the surface area of two similar cylinders is 16:25, what is the ratio of their volumes?
2) If the ratio of the perimeters of two similar triangles is 2:9, what is the ratio of their areas?
3) If the ratio of the volumes of two similar spheres is 125:8, what is the ratio of their areas?
4) If the ratio of the surface areas of two similar rectangular boxes is 4:9, what is the volume of the larger box if the
volume of the smaller box is 26 m3? (round to the nearest tenth, if necessary)
5) If the ratio of the volumes of two cylinders is 8 : 343, what is the area of the smaller cylinder if the area of the
larger cylinder is 98 m2?
6) If the ratio of the perimeters of two similar spheres is 4 : 5, what is the volume of the larger sphere if the volume
of the smaller sphere is 75 in3 ? If necessary, round your answer to the nearest hundredth.
Not-So-Formal Proofs:
1)
has angles with measures of 60 degrees and 80 degrees.
and 50 degrees. Are these triangles similar?
has angles with measures of 80 degrees
2) Show that the two triangles are similar.
3) Determine if the right triangles below are similar.
Justify your answer.
4) Is
5) Is
? Explain.
? Explain.
6) Which of the followng side lengths coould represent two similar triangles?
(a)
12 in, 8 in, 6 in
: 24 in, 16 in, 10 in
(b)
9 in, 4 in, 8 in
: 13.5 in, 6 in, 12 in
(c)
5 in, 7 in, 11 in
: 12.5 in, 14 in, 27.5 in
(d)
7 in, 12in, 9 in
: 5.25 in, 9 in, 4.5 in
Similar Triangle Proofs:
1) Given:
Prove:
2) Given:
Prove:
is isosceles with base AC
3) Given:
Prove:
4) Given:
Prove:
5) The diagram below shows
, with
and
. Prove that
is similar to
Name:__________________________________________________________
Review Sheet
Date:_______________________ Period:__________
Geometry Honors
Directions: Answer the following questions completely. Please remember to show all work that is necessary for the
test.
1) Given:
Prove:
2) In a triangle, the measure of the first angle is
less than the measure of the second one, and the
measure of the third angle is twice as great as the
measure of the first one. What are the measures of
the angles of the triangle?
3) Farmington, NY, has plans for a new triangular
park. If plotted on a coordinate grid, the vertices
would be A(3,3), B(5,-2), and C(-3,-1). However, a
tract of land has become available that would enable
the planners to increase the size of the park, which is
based on the following transformation of the original
triangular park,
. On the grid to the right, graph
and label both the original park
and its image, the
new park
, following the transformation.
4) Dorothy says that two angles in a triangle she drew
have the measures
and
. Can Dorothy be right
about her triangle? Explain why or why not.
5) Given
,
, and
?
6) For question number 6, use the diagram to answer the questions that follow.
(a) What is the length of ?
(b) What is the length of
?
(c) What is the length of ?
(d) What is the perimeter of
?
,
, what is
7) In the diagram below,
bisects angle ADF. Use the
angle measures given on the diagram to find the angles
of triangle ADE.
8) Find the equation of a line that is perpendicular
to
and passes through the point
(-4,8).
9) The diagram shows two moves of a checkers piece.
Describe its movement as a translation. Use the row and
Column numbers as coordinates.
10) Using a compass and a straightedge, construct an
angle bisector. [Leave all construction marks.]
11) On the ray drawn below, using a compass and a straightedge, construct an equilateral triangle with a vertex at
R. The length of a side of the triangle must be equal to a length of the diagonal of rectangle ABCD. [Leave all
construction marks.]
Answer Key:
Ratio of Similitude:
1.) 30
2.) 28
3.) 14 m
4.) 5, 8, 6
5.) 10
6.) (c)
7.) (c)
8.) 9.7
Overlapping Triangles:
1.) 40
2.) x = 4; FJ = 10
3.) 1.75
4.) 10
5.) 2.7
Midsegment:
1.) (1)
2.) (3)
3.) (a) 79o
(b) 67o
(c) 34o
(d) 146o
4.) (a) 9 inches (b) No because his hand is not half the length of the rabbit shadow
5.) k = 9; XY = 26
6.) correct construction
Ratio of Similarity:
1.)
2.)
3.)
4.) 87.8 m3
5.) 8m2
6.) 146.48 in3
Not-So-Formal Proofs:
1.) No, not all of the angle measures are congruent.
2.) SAS~
5.) Not similar because not all of the sides are in proportion.
3.) SAS~
4.) SSS~
6.) (b)
Similar Triangle Proofs (Formal):
1.) Statements:
Reasons:
Given
Intersection lines form congruent vertical angles.
AA
2.) Statements:
is isosceles with base AC
Reasons:
Given
Base angles of an isosceles triangle are congruent.
Perpendicular lines meet to form congruent right angles.
AA
Corresponding sides of similar triangle are in proportion.
3.) Statements:
,
Reasons:
Given
Parallel lines cut by a transversal form congruent alternate interior angles.
AA
Corresponding sides of similar triangle are in proportion.
The product of the means equals the product of the extremes.
4.) Statements:
;
Reasons:
Given
Perpendicular lines form congruent right angles.
AA
Corresponding sides of similar triangle are in proportion.
The product of the means equals the product of the extremes.
5.) Statements:
;
Reasons:
Given
Reflexive
AA
Review Topics
1.) Statements
BD is an altitude of
BD is a median of
Reasons
Given
An altitude creates congruent right angles.
A median divides a segment into two congruent segments.
Reflexive
SAS
2.) 54o, 42o, 84o
3.) A”(6,-6), B”(-4,-10), C”(-2,6)
5.) x = 36; m<8=74o
6.) (a) 11
7.) m<EAD = 48o, m<ADE = 66o, m<DEA = 66o
10.) correct construction
(b) 11
(c) 13
8.)
11.) correct construction
4.) No, there is only 180o in a triangle.
(d) 34
9.)