Download Math 310 Practice Test 2

Math 310 Practice Test 2
1. a. Measure the following angle to the nearest degree: (do some more examples in your text)
b. Is the angle acute, right, or obtuse?
2.
b.
c.
d.
a. Fill in the blanks: 1◦ = −−0 and 10 = −−00
If the measure of an angle is 35◦ 450 2200 , what is the measure of its supplement?
The measure of an angle is 13◦ 490 2700 . Find the measure of its complement.
Find 113◦ 570 + 18◦ 140
3. In the following statements, determine whether it is TRUE or FALSE. If FALSE, provide a counterexample
(i.e., draw an example that shows the statement is false).
a. All rectangles are squares.
b. Every square is a rhombus.
c. All triangles are convex.
d. A regular quadrilateral is a square.
e. No rectangle is a rhombus.
f. The diagonals of a rhombus are perpendicular bisectors of each other.
4.
a.
b.
c.
If possible, draw the following triangles. If it is not possible, explain why.
An obtuse isosceles triangle.
A right equilateral triangle.
An acute scalene triangle.
5.
b.
c.
d.
a. What is the measure of the sum of the interior angles of a regular hexagon?
What is the measure of each interior angle of a regular hexagon?
What is the measure of each exterior angle of a regular hexagon?
What is the sum of the measures of all exterior angles of a regular hexagon?
6. Sketch a net for the following polyhedra. Identify the number of VERTICES, EDGES and FACES for each.
Check your answers with Euler’s Formula: V + F − E = 2
a. right triangular prism
b. right hexagonal prism
c. right triangular pyramid
d. cube
e. right square pyramid
f. right pentagonal prism
g. right dodecagonal pyramid (a dodecagon has 12 sides)
h. right trapezoidal prism
7. Draw a few examples of planar figures that aren’t polygons. Draw a few examples that are.
1
8.
a.
b.
c.
d.
Using the Triangle Inequality, determine whether the following lengths can possibly form a triangle.
5cm, 3cm, 1cm
10m, 12m, 5m
3ft, 4ft, 5ft
100in, 88in, 12in
9. Determine x assuming m and n are parallel. Show all of your work clearly.
10. Put the following in the empty boxes to show the relationship among the terms:
parallelogram, quadrilateral, isosceles trapezoid, rectangle, rhombus.
11. Consider the parallelogram PQRS (the first image). The two images that follow each have one diagonal drawn.
For each, find a pair of congruent triangles and justify why they are congruent. Carefully explain all reasoning.
12. Find the measure of the third angle in each of the following triangles.
a. 30◦ , 60◦
b. 45◦ , 45◦
c. 23◦ , 47◦
2
d. 11◦ , 109◦
13. a. If one angle of a triangle is obtuse, can another also be obtuse? Why or why not?
b. If one angle in a triangle is acute, can the other two angles also be acute? Why or why not?
c. Can a triangle have two right angles? Why or why not?
d. If a triangle has one acute angle, is the triangle necessarily acute? Why or why not?
14. Suppose you have a convex nonagon with the following interior angle measures:
205◦ , 142◦ , 122◦ , 130◦ , 110◦ , 108◦ , 143◦ , 150◦ . Find the measure of the remaining interior angle.
15. Suppose a regular polygon has an exterior angle measure of 2◦ . How many sides does the polygon have? What
is the interior angle sum?
16. Find ALL missing angles in the diagram below. You may assume that the three lines are parallel.
17. A rancher designed a wooden gate as illustrated in the following figure. Explain the purpose of the diagonal
boards on the gate. (see pg 659)
18. In the rectangle ABCD shown, X and Y are midpoints of the given sides.
What type of quadrilateral is PYQX? Prove your answer.
3
19. Let 4ABC be an isosceles triangle, where A is the point ”on top”.
a.
b.
c.
d.
Draw the angle bisector of < A, and call the intersection of this line and the base D
Prove that 4ADB ∼
= 4ADC. Explain it clearly, listing any congruent sides and/or angles.
Why is BD = CD?
Why is < BDA ∼
=< CDA?
CONSTRUCTIONS:
Know how to do the following constructions:
1. a circle with a given center and radius
2. a congruent line segment
3. construct a triangle congruent to a given triangle (you can use the SSS property)
4. copy an angle
5. perpendicular bisector
6. parallel lines
7. bisect an angle
8. construct perpendicular lines (given a line and a point NOT on the line)
9. construct perpendicular lines (given a line and a point ON the line)
10. bisect a line segment (same construction as perpendicular bisector)
11. construct an altitude of a triangle (this is actually the same construction as #8, it is simply a matter of looking
at it appropriately.)
4