Download GEOMETRY END OF COURSE ASSIGNMENT

1. You are on a jungle expedition and come to a raging river. You need to build a bridge across
the river. You spot a tall tree directly across from you on the opposite bank (point ). You
place a pole in the ground to mark the position directly across from the tree. From the spot
you are standing, you walk directly downstream 16 feet and place another pole (point ). You
keep walking down stream and mark a third spot with a pole that is 7 feet from your last pole
(point ). Turning perpendicular from the last pole, you walk away from the river 9 feet to
another position and place a fourth pole (point ).
a. Determine if the two triangles are similar. Explain which similarity theorem you used and
why.
b. Use proportions to calculate the distance across the river.
A large tree is close to point and we could chop it down at an angle to reach point and
safely cross the river.
c. How tall does the tree need to be to span the river from point to ?
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2. This figure shows a quadrilateral made of
and
.
a. What does it mean for triangles to be congruent?
b. Jane is told that
is congruent to
and
is congruent to
She concludes that the
triangles are congruent because of AAA. Explain why she thinks this, and whether or not you
think she is right.
c. George is told the same thing as Jane, but he concludes that the triangles are congruent
because of ASA. Explain why he thinks this, and whether or not you think he is right.
d. Are there any other ways the two triangles could be congruent with the information Jane
and George have been given? Explain why you think this.
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3. To win a local billiards tournament, all Jeanette has left to do is drop the 9-ball. Because of
the other balls on the table (not shown), her only realistic shot on this turn is to bounce the
ball off both sides of the table as shown. Use the information in the image to answer the
questions below. Lines
far side.
and
are parallel, and the near side of the table is parallel to the
a. What other angle measures can we be sure about? Explain your reasoning.
b. Identify the sets of congruent angles. Explain your conclusions.
c. Identify all the sets of alternate interior angles you can envision. Explain.
d. Identify all the sets of corresponding angles. Explain.
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4. You are a botanist studying a rare flower. The center of the flower is a regular polygon. The
petals coming off the flower are roughly triangular in shape.
a. What is the name of the center polygon?
b. What is the sum of the interior angles of the center?
c. What is the measure of each interior angle of the center?
d. In order to compare the size of the petals to other flowers of the same species you need to
determine the exterior angle of the polygon. What is the measure of the exterior angle of the
polygon?
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5. Name and classify the basic geometric object each real life object represent using correct
mathematical notation.
a. The location of a city on a map
b. The angle of a recliner
c. Row of corn in a garden
d. The angle of a lawn chair when laid all the way down
e. An arrow
f. The angle of a jet taking off at an airport
g. The angle a flag pole sits with the ground
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6. Decide whether each statement is true or false. If a statement is true, say which of Euclid’s
five postulates apply to it, then write the converse and contrapositive statements, and then
decide which of these statements are true (it may help to rewrite the statements in “if-then”
form). If it is false, give a counterexample or explain why.
a. A triangle can be drawn from any three points that are not on the same line.
b. A square can be drawn from any four points not on the same line.
c. When two lines intersect, the four angles they make add to 360 degrees.
d. There is only one parallel line to any given line.
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7. You are building a gazebo for your mom; you want it to look like the picture below.
a. Using geometry, name which quadrilaterals you see in the picture.
b. What type of quadrilateral is each side of the roof (see inset)?
c. What specific type must it be in order for each side of the roof to fit properly?
d. What is the length of the opposite leg on the side of the roof?
e. What measure is the other base angle?
f. What is the measure of the opposite angles?
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