GEOMETRY Chapter One
True–False. Mark as true any statement that is always true. Mark as false any statement that is
never true or that is not necessarily true. Be able to justify your answers.
1. An “exercise” can be solved by simply applying a routine procedure, but a “problem” is not
routine and requires a well-thought-out plan of attack.
2. If there are infinitely many numbers involved in a problem, the Guess and Test problem-solving
strategy is indicated.
3. If 12 coins are arranged in the shape of an equilateral triangle, then there are 5 coins along
each side.
4. If the fourth phase of problem solving, “Looking Back,” we should look for other ways to solve
the problem even if we got the ‘right’ answer.
5. When you are asked to make a generalization, you should use the Guess and Test
problem-solving strategy.
6. If a problem involves a large array or diagram, a good strategy to try is “Use a Variable.”
7. If a problem involves a physical situation, the “Draw a Picture” strategy may be appropriate.
8. If a problem involves a sequence of numbers or figures, the “Draw a Picture” strategy may be
appropriate.
9. If a problem asks you to make a prediction or generalization, the “Look for a Pattern” strategy
may be appropriate.
10. If a problem asks “in how many ways” the “Look for a Pattern” strategy may be appropriate.
11. The fourth term in the sequence 3, 5, 7, . . . must be 9.
12. If a large cube is made up of 64 smaller cubes, then it has 16 cubes showing on each face of the
larger cube.
13. Patterns in data may be easier to see if we arrange the data in tables.
Multiple Choice. Mark the letter of the single BEST response. Be sure to read all the choices for
each problem before deciding.
14. George Polya presented a four step process for problem solving which is still used extensively
today. Which of the following is NOT a step in his basic process?
(a) Devise a plan.
(b) Understand the problem.
(c) Carry out your plan.
(d) Draw picture.
(e) Look back to analyze your solution.
15. The Guess and Test problem-solving strategy can be useful when
(a) there are only a few possible solutions to a problem.
(b) the problem suggests an equation.
(c) you are trying to develop a formula.
(d) you need to find the measures of the angles in a triangle.
(e) there is an unknown quantity related to known quantities

16. You may wish to use the “Solve a Simpler Problem” strategy if:
(a) The problem involves very large or very small numbers.
(b) There are a large number of cases.
(c) A direct solution is too complex.
(d) Both (a) and (b) are correct.
(e) Both (a) and (c) are correct.
17. When using the Guess and Test Problem Solving Strategy you will probably be most successful
if you
(a) simply try possibilities at random.
(b) use a means of organizing your guesses.
(c) try to learn from each of the trials.
(d) apply both parts (a) and (c).
(e) apply both parts (b) and (c).
18. If a problem asks “how many cubes are in the nth figure,” an approach to solving the problem
might be:
(a) Guess and Test.
(b) Draw a Picture.
(c) Make a Table.
(d) Look for a Pattern.
(e) Use a Variable.
19. If a problem asks you to “Find a formula . . . “ you might begin by
(a) drawing a sketch of the problem situation.
(b) understanding the terms used in the problem.
(c) looking for relationships between known quantities and the unknown quantity.
(d) making a tables of values, using n as the unknown quantity.
(e) trying any one of the above.
20. If you are given a sequence of numbers and asked to predict the next number in the sequence,
a problem solving strategy you might reasonably try is
(a) Look for a Pattern.
(b) Draw a Picture.
(c) Guess and Test.
(d) Trial and Error.
(e) None of these is a particularly good strategy.
21. If a problem begins with “There are 200 people at a dance . . .”, an approach to solving the
problem may be
(a) Draw a Picture.
(b) Guess and Test.
(c) Solve a Simpler Problem.
(d) Deductive reasoning.
(e) None of these is a good approach.
22. When we look at specific examples, observe a pattern, and draw a general conclusion, we are
using
(a) the Draw a Picture problem-solving strategy.
(b) Deductive reasoning.
(c) the Use a Variable problem-solving strategy.
(d) The Guess and Test problem-solving strategy.
(e) Inductive reasoning.
2 Chapter 1

23. Deductive reasoning requires us to
(a) accept some initial conditions as true.
(b) make a table.
(c) look for a pattern.
(d) solve a simpler problem.
(e) draw a picture.
24. When using formal problem-solving strategies, we
(a) must choose the right one for the problem.
(b) should not mix them in one problem.
(c) should always start by choosing a variable.
(d) are using deductive reasoning.
(e) None of these answers is always true.
Fill in the Blanks. Complete each statement with a word or phrase that makes it true.
25. When solving a problem with geometric figures involved, we should use the
problem-solving strategy.
26. When solving a problem in which you can easily present information, we should use the
problem solving strategy.
27. If you wish to gain a better understanding of a complex problem, you might use the
problem solving strategy.
28. The sum of the measures of the angles in a triangle is .
29. When a problem asks us to predict a sequence of numbers or figures, we should use the
problem-solving strategy.
30. If we start with some general statements accepted as true and then draw conclusions from
them, we are using reasoning.
31. If we are using reasoning, our answer may not be the only
correct one.
Writing. Write your answers concisely and completely. Feel free to use figures and/or tables to
illustrate the points you are making.
32. List the four steps in the problem-solving process first introduced by George Polya and
employed in all the problem-solving strategies.
33. Read and solve the following problem. Then write a paragraph describing the method you
used to get your solution. Which problem-solving strategy(s) did you use and why?
At a family dinner Grandmother, Aunt Suzie, Mary, Father and Richard are to
sit along one side of the table. Grandmother must sit on one end. Aunt Suzie and
Richard cannot be seated next to each other. Aunt Suzie wants to sit next to
Mary. Mary must sit next to Grandmother. How should their seating
arrangements be made?
34. Read and solve the following problem. Then write a paragraph describing the method you
used to get your solution. Which problem-solving strategy(s) did you use and why?
Toothpicks can be arranged to form rows of rectangles as shown. How many
toothpicks are required to form a row with 30 rectangles in it?
Chapter 1 3

35. Compare and contrast inductive and deductive reasoning.
36. Read and solve the following problem. Then write a paragraph describing the method you
used to get your solutions. Which problem solving strategies did you use and why?
The heptagonal numbers are the whole numbers that represent the following shapes.
Find the number of dots in the nth heptagonal number.
37. Read and solve the following problem. Then write a paragraph describing the method you
used to get your solution. Which problem-solving strategy(s) did you use and why?
How many triangles of all sizes are there in the figure below?
Exercises and Problems.
38. A large cube is formed by arranging 27 smaller white cubes of the same size into a cube shape.
If three faces which share one corner of the larger cube are painted red, how many of the
smaller cubes will have exactly two red faces?
39. If all the diagonals are drawn in a polygon with five sides (a pentagon), what is the maximum
number of intersections of two diagonals?
40. The measure of one angle of a triangle is twice the measure of a second angle. The measure of
the third angle is twelve degrees more than the measure of the first angle. What is the measure
of the largest angle of the triangle?
41. Samuel, Martha, James, Katie and Rafael all go to the movies. James insists on sitting on the
aisle. Samuel and Martha must sit next to each other. Rafael sits next to Samuel and next to
James. Who is sitting next to Katie?
42. How many squares of all sizes are there in a 4 by 4 square? Sketch all of the squares on the
provided 4 by 4 squares and briefly explain your work.
Heptagonal Number
1 2 3 4 n?
4 Chapter 1

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Test Bank For College Geometry: A Problem Solving Approach with Applications, 2nd Edition

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