Chapter 2 Practice
ProblemsName:_________________________________
Concept Problems
1. The diagrams below are not necessarily drawn to scale. For
each pair of triangles:
· Determine if the two triangles are congruent.
· If the triangles are congruent, write a congruence statement
(such as ΔPQR ≅ ΔXYZ) and give the congruence theorem
(such as SAS ≅).
· If the triangles are not congruent, or if there is not enough
information to determine congruence, write “cannot be
determined” and explain why not.
AC is a straight segment:
2. Misty is building a triangular planting bed. Two of the
sides have lengths of eight feet and five feet. What are the
possible lengths for the third side?
Concept Problems
1. In an isosceles triangle, the two angles opposite the
congruent sides are called the base angles. You may have
learned in a previous course that the base angles of an isosceles
triangle are always congruent. Now you will prove it!
In the diagram at right, ∆ SYM is an isosceles triangle,
and point E is the midpoint
of SM .
1. Make a flowchart to prove that the base angles of
∆ SYM are congruent, that is, prove that ∠S ≅
∠M.
2. Determine the area of each of the following
figures. Assume that all angles that look like right angles
are right angles.
3. Complete each of the Diamond Problems below.
a.
b.
c.
d.
4. Use your knowledge of angle pair relationships to write
an equation and solve for x in the diagrams below.
Then calculate the measures of the labeled angles. Justify
your solutions by naming the theorem.
Concept Problems
1. Write a converse for each conditional statement
below. Then, assuming the original statement is true, decide
if the converse must be true or not.
a. If it rains, then the ground is wet.
b. If a polygon is a square, then it is a rectangle.
c. If a polygon is a rectangle, then it has four 90° angles.
d. If a polygon has three angles, it is a triangle.
e. If two lines intersect, then vertical angles are
congruent.
2. Solve for x in each diagram below.
3. The set of equations at right is an example of
a system of equations.
Solve the system using an algebraic method of your choice
(substitution or elimination).
4. Determine whether or not the triangles in each pair
below are congruent. Justify your conclusion with a triangle
congruence theorem.
Concept Problems
1. Complete each of the Diamond Problems below.
2. Solve each equation below. Show all work and
check your answers.
a.
b.
c.
d.
3. Examine the two triangles at
right.
a. The triangles are congruent. Justify by giving the triangle
congruence theorem.
a. Write a congruence statement
4. The dashed line at right represents the line of
symmetry of the shaded figure. Calculate the area and
perimeter of the shaded region. Show all work.
5. Examine the figure at right, which is not drawn to
scale. Which is longer, AB or BC?
Explain your answer.
Concept Problems
1. While waiting for a bus after school, Renae programmed
her MP3 player to randomly play two songs from her playlist, at
right. Assume that the MP3 player will not play the same song
twice.
a. Are each of the combinations of two songs equally
likely?
b. Calculate the probability that Renae will listen to two songs
with the name “Mama” in the title.
c. What is the probability that at least one of the songs will
have the name “Mama” in the title
d. Why does it make sense that the probability in part (d) is
higher than the probability in part (c)?
2. Plot triangle ABC with
vertices A(0, 0), B(3, 4), and C(3, 0) on graph
paper. Using the origin as the point of dilation, enlarge it
by a factor of 2. On a new graph plot this new triangle and label
it A'B'C'.
a. What are the side lengths of the original
triangle, ΔABC?
a. What are the side lengths of the enlarged
triangle, ΔA'B'C'?
a. Calculate the area and the perimeter of
ΔA'B'C'.
3. Fill in the missing dimensions and areas. Then
write the area as a product equal to the area as a
sum.
a.
b.
Concept Problems
1. For each triangle below, solve for the variable
and answer the questions.
a. Solve for x. What kind of triangle is
∆ABC? Be specific.
b. Solve for y. What kind of triangle is shown in the
figure? Be specific.
2. If you enlarge the shape at right from the origin by
a scale factor of 4, what are the new coordinates?
3. Look at the similar triangles below. Write ratios
(fractions) for the corresponding side lengths.
a. Calculate the length of the hypotenuse of each
triangle. Is the ratio of the hypotenuses equal to the ratios
you found?
4. Examine each diagram below. Identify the
error in each diagram.
5. Complete each of the Diamond Problems below.
a.
b.
c.
d.
Concept Problems
1. TOP OF THE CHARTS
Renae’s MP3 player can be programmed to randomly play songs from
her playlist without repeating a single song. Currently, Renae’s
MP3 player has five songs loaded on it which are listed at
right. At the moment, she only has time to listen to one
song.
Is each song equally likely to be chosen as the first song?
What is the probability that her MP3 player will play a country
song?
What is the probability that Renae will listen to a song with
“Mama” in the title?
What is the probability that she listens to a duet with Hank
Tumbleweed?
What is the probability that she listens to a song that is not R
& B?
2. Decide if each pair of triangles below is
similar. If the triangles are similar, justify your
conclusion by stating the similarity condition you used.
Also, describe a possible sequence of transformations that would
carry one onto the other. If the triangles are not similar,
explain how you know they are not similar.
Concept Problems
1. Fill in the missing dimensions and areas. Then write
the entire area as a product equivalent to the area as a
sum
2. Assume that each pair of figures below is similar.
Write a similarity statement to illustrate which parts of each
shape correspond. Remember, letter order is
important!
3. Determine which of the following pairs of
triangles are similar. Justify your answer with a similarity
theorem.
4. Based on the measurements provided for each
triangle below, determine whether the measure of x must
be more than, less than, or equal to 45º
Concept Problems
1. Determine which similarity conditions (AA ~,
SSS ~, or SAS ~) could be used to establish that the
following pairs of triangles are similar. List as
many as you can.
2. Why are the two triangles similar?
3. If two sides of a triangle are 8" and 13" long, what do
you know about the length of the third side?
4. Use the triangles at right to answer the following
questions. Are the triangles at right
similar?
a. How do you know if they are similar? Show your
reasoning in a flowchart.
a. Examine your work from part (a). Are the triangles also
congruent? Explain why or why not.
Concept Problems
1. Multiply each expression
2. Solve for the missing lengths. Show all
work.
a. ΔGHI ~ ΔPQR b.
ΔABC ~ ΔXYZ
3. Which pairs of triangles below are congruent and/or
similar? For each part, explain how you know using an
appropriate triangle congruence or similarity condition.
Note: The diagrams are not necessarily drawn to scale.
4. Which of the following events are
independent? Two events are independent if knowing
that one event occurred does not affect the probability of the
other event occurring.
a. Flipping five heads in a row and then flipping another
head.
a. Drawing two aces from a deck of cards without replacing them
and then drawing another ace.
a. It rains this weekend, and the debate team from North City
High School wins the state championship.
a. Your friend selects a diet soda from a cooler of mixed
beverages and then you select a diet soda from the same cooler
without looking
9
(3)(21)
xx
++
2(5)
xx
+
(2)
xxy
+
(25)(2)
xxy
+++
