Multiple Choice Identify the
choice that best completes the statement or answers the question.


1.

Lines s, t, and u are perpendicular bisectors of the
sides of and meet at J. If , , and ,
find x, y, and z.
a.  x = 1, y = 5, z = 5  c.  x = 5, y = 1,
z = 5  b.  x = 2.5, y = 2, z = 2.3  d.  x = 0, y = 6, z =
2.3 


2.

is an altitude, , and . Find .


3.

is an angle bisector, , , and . Find
. Is an
altitude?
a.  50; no  c.  47; yes  b.  32; no  d.  17.3; no 



Determine the relationship between the measures of the given
angles.


4.



5.




Determine the relationship between the lengths of the given sides.


6.

a.   c.  cannot be
determined  b.   d.  


7.




Determine whether the given measures can be the lengths of the sides of a
triangle. Write yes or no. Explain.


8.

3, 9, 10
a.  Yes; the third side is the longest.  b.  No; the sum of the lengths of two sides is not
greater than the third.  c.  No; the first side is not long
enough.  d.  Yes; the sum of the lengths of any two sides is greater than the
third. 


9.

9.2, 14.5, 17.1
a.  Yes; the third side is the longest.  b.  No; the first side is not long
enough.  c.  Yes; the sum of the lengths of any two sides is greater than the
third.  d.  No; the sum of the lengths of two sides is not greater than the
third. 


10.

An isosceles triangle has a base 9.6 units long. If the congruent side lengths
have measures to the first decimal place, what is the shortest possible length of the sides?


11.

Which segment is the shortest possible distance from point D to plane
P?

Short Answer



Write a twocolumn proof.


12.



13.

If is a median of isosceles ,
then .


14.

If is a median and a perpendicular bisector of
, then .



Write an indirect proof.


15.

Given: Prove:


16.

Given: Prove: is
positive.


17.



18.

If n is a multiple of 9, then it is a multiple of 3.


19.

If , then .


20.

If is an integer, then n is
even.


21.

Given: is an even number. Prove: n
is an even number.


22.

Given: Prove:


23.

Given: Prove:


24.

Given: Prove:


25.



26.



27.



28.

Given: ; A is the midpoint of BF and
CD. Prove:


29.



30.

Given: is a perpendicular bisector of equilateral
triangle . is a median of . Prove:


31.

Given: Square GHJKProve:


32.



33.

Given: is a perpendicular bisector of . Prove: is isosceles


34.




Write a twocolumn proof.


35.



36.



37.



38.



39.

A circular swimming pool needs to be designed for a triangular lawn surrounded
by apartment buildings at the three corners, as shown in the figure below. The swimming pool should
be located such that the center of the pool is equidistant from the buildings at the corners.
Describe the position of the swimming pool.


40.

Three children are playing a game on the playground. They stand on the
playground facing each other. They want to place a ball on the playground so that it is equidistant
from each of the three children. Describe the position of the ball.


41.

In the figure below, is an angle bisector of
and is a
perpendicular bisector of R is the point of intersection of and Show that


42.

In the figure below, rectangle ABCD represents a wall. The following
clues are given about the position of a painting on the wall. (1) The painting is as far
from point A as it is from point B. (2) If you
measure the distance from point D to the painting or from point C to the painting, you
would measure the same distance.
Describe the position of the painting.


43.

Samantha and her friends are playing carrom, a board game in which players slide
pieces to hit other pieces. Samantha hits a piece called the queen. The new position of the queen is
given by the following clues (1) The queen is as far from point P as it is from
point Q. (2) If you moved straight along SP to
the queen or along SR to the queen, you would move the same distance.
Describe
the position of the queen.


44.

A salesperson travels from city A to city B and then to city C. From city C, the
salesperson travels directly back to city A as shown in the diagram below. Write the lengths of the
legs of the trip in order from least to greatest.


45.

Triangle ABC has vertices and
List the angles in order from the greatest to the least measure.


46.

A triangle is formed by three kitchen appliances as shown in the figure. The
distances shown are measured in feet. What is wrong with the labels on the triangle?


47.

A tree 44 meters high cast a shadow 60 meters long, as shown below. Write an
inequality relating x and y. Then solve the inequality for x in terms of
y.


48.

In the figure below, the length of BF is given by
and the length of AF is given by Write an inequality relating x and
y. Then solve the inequality for y in terms of x.


49.

Prove that has no more than one obtuse angle.


50.

Samantha and Nick have rectangular rooms with the same perimeter.
Samantha’s room is 9 feet by 12 feet. The length of Nick’s room is 8 feet. Prove that
the width of Nick’s room is less than 14 feet.


51.

On a field trip, of the students have jackets. If there are 20
students on a field trip, verify that 15 students have jackets.


52.

Lauren, Rose, and Keith worked at the facepainting booth at the Fall Festival.
Lauren painted 13 faces, Rose painted 29 faces, and Keith painted 15 faces. Has Rose painted more
faces than the total number of faces painted by Lauren and Keith?


53.

Megan and Sara took part in a 500meter race on sports day at the school. As the
race finished, Megan claimed that she was the winner of the race. The teacher said that according to
the stopwatch, Megan took 10 minutes to complete the race, whereas Sara completed the race in 9
minutes. So, Megan was not the winner of the race. Explain whether this is an example of indirect
reasoning.


54.

Two sides of a triangle are 3 feet and 4 feet long. Let x represent the
measure of the third side of the triangle. Suppose x is whole number such that
List the measures of the sides of the triangles that are possible.


55.

One side of a triangle is 5 feet long. Let x represent the measure of the
second side and let y represent the measure of the third side. Suppose x and y
are whole numbers and that and List the
measures of the sides of the triangles that are possible.



John has five straws. He wishes to use the straws to make a triangular
design. The straws measure 6 centimeters, 2 centimeters, 7 centimeters, 8 centimeters, and 13
centimeters.


56.

How many different triangles could John make with the straws?


57.

How many different triangles with even perimeters could John make?


58.

The two sides of a triangle are 3 feet and 6 feet long. Let b represents
the measure of the third side. List a possible range for b.


59.



60.

Measure the distance between the handles of a pair of scissors as shown in the
picture below. Now, apply force to the handles of the scissors to cut a piece of paper and measure
again. How do the measures compare?


61.

The figure below shows the position of two planes, plane 1 and plane 2, after
traveling 170 miles in different directions from the airport marked by P. Which plane is
farther from the airport?


62.



63.

Let represent the legs of a tripod. Assume the
legs are congruent and Compare the lengths of
