Questions

1) The definition of an inequality states that for any real numbers, a and b, a > b if and only if there is a positive number c, such that __________.

a.) a = b + c

b.) a = b – c

c.) a = b

d.) a = c

2) True or False: The comparison property or the inequalities of real numbers is: a < b, a = b, or a > b.

True

False

3) In the transitive property of the inequalities of real numbers, if a < b, and b < c, then __________ OR if a > b, and b > c, then __________.

a.) a < c, a < c

b.) a > c, a > c

c.) a > c, a < c

d.) a < c, a > c

4) In the addition property of the inequalities of real numbers, if a > b, then a + c ____ b + c OR if a < b, then a + c ____ b + c.

a.) <, >

b.) <, <

c.) >, >

d.) >, <

5) In the subtraction property of the inequalities of real numbers, if a > b, then a – c ____ b – c OR if a < b, then a – c ____ b – c.

a.) <, >

b.) <, <

c.) >, >

d.) >, <

6) In the multiplication properties of the inequalities of real numbers, if “c” is positive and a < b, then ac ____ bc OR if “c” is positive and a > b, then ac ____ bc.

a.) <, >

b.) <, <

c.) >, >

d.) >, <

7) In the multiplication properties of the inequalities of real numbers, if “c” is negative and a < b, then ac ____ bc OR if “c” is negative and a > b, then ac ____ bc.

a.) <, >

b.) <, <

c.) >, >

d.) >, <

8) In the division properties of the inequalities of real numbers, if “c” is positive and a < b, then (a/c) ____(b/c) OR if “c” is positive and a > b, then (a/c) ____ (b/c).

a.) <, >

b.) <, <

c.) >, >

d.) >, <

9) In the division properties of the inequalities of real numbers, if “c” is negative and a < b, then (a/c) ____(b/c) OR if “c” is negative and a > b, then (a/c) ____ (b/c).

a.) <, >

b.) <, <

c.) >, >

d.) >, <

10) Select the property that justifies the statement.

a.) Comparison

b.) Transitive

c.) Addition

d.) Subtraction

11) Select the property that justifies the statement.

a.) Comparison

b.) Transitive

c.) Addition

d.) Multiplication

12) Select the property that justifies the statement.

a.) Comparison

b.) Transitive

c.) Subtraction

d.) Division

13) Select the property that justifies the statement.

a.) Comparison

b.) Transitive

c.) Subtraction

d.) Division

14) Select the property that justifies the statement.

a.) Comparison

b.) Transitive

c.) Multiplication

d.) Division

15) Select the property that justifies the statement.

a.) Comparison

b.) Transitive

c.) Multiplication

d.) Division

16) Point U lies on segment TV between points T and V as shown in the figure below. Complete the following statements: (a) Segment TU is less than _____. (b) Segment UV is greater than segment _____. (c) Segment UV is less than segment _____.

250 character(s) left
Your answer is too long.

17) Point U lies in the interior of angle RST as shown in the figure below. Ray SU is between rays SR and ST. Complete the following statements: (a) The measurement of angle UST is less than the measurement of angle _____. (b) The measurement of angle RSU is greater than the measurement of angle _____. (c) The measurement of angle RSU is less than the measurement of angle _____.

250 character(s) left
Your answer is too long.

18) Bill is going to purchase a tractor and backhoe attachment for a payment of $625 MONTHLY for 3 years. His goal is to finance, at most, $20,000. Write an inequality comparing ”the amount he must pay back in all” to “$20,000”, and then state whether he has met his goal.

4000 character(s) left
Your answer is too long.

19) For the purchase described in the previous problem, how much money must Bill pay for a down payment to meet his goal?

250 character(s) left
Your answer is too long.

20) Fill in the blank. Theorem 15-A: If an angle is an exterior angle of a triangle, then its measure is greater than the measure of either of its __________.

250 character(s) left
Your answer is too long.

21) A partial “indirect” proof of the Exterior Angle Inequality Theorem is shown in the unit link to “Inequalities”. An incomplete proof of Cases 3 and 4 are shown below. State the number and the corresponding statement or reason of each of the five missing parts of the proof.

4000 character(s) left
Your answer is too long.

22) Refer to the figure below to answer the following questions. (The figure is drawn to scale.) (a) Which is greater, the measurement of angle 5 or the measurement of angle 3? (b) State one angle that is less than the measure of angle 2.

250 character(s) left
Your answer is too long.

23) Fill in the blank. Theorem 15-B: If a side of a triangle is longer than another side, then the measure of the angle opposite the longer side is greater than the measure of the __________.

250 character(s) left
Your answer is too long.

24) Read the two theorems (15-B and C) in the link to “Triangle Side and Angle Inequalities”, and then select the statement that is NOT true.

a.) In a triangle, if one side is longer than another, then the angle opposite the longer side is greater than the angle opposite the shorter side.

b.) In a triangle, if the measure of one angle is greater than the measure of a second angle, then the side opposite the greater angle is shorter than the side opposite the smaller angle.

c.) In a triangle, if the measure of one angle is greater than the measure of a second angle, then the side opposite the greater angle is longer than the side opposite the smaller angle.

25) What are the lengths of segments (a) ST, (b) TR, and (c) RS? Round each answer to the nearest tenth.

250 character(s) left
Your answer is too long.

26) Fill in the blanks for the statement shown below.

250 character(s) left
Your answer is too long.

27) What is (a) the value of “x”, (b) the measure of angle L, (c) the measure of angle M, and (d) the measure of angle N?

250 character(s) left
Your answer is too long.

28) Select the inequality statement that compares the lengths of the three sides of the triangle from largest to smallest.

a.) MN > LM > NL

b.) ML > MN > NL

c.) LM > NL > MN

d.) MN > NL > LM

e.) LM > MN > NL

29) In an obtuse scalene triangle, one angle measures 50 degrees. Which side is this angle opposite?

a.) longest side

b.) shortest side

c.) other side that is in between longest and shortest sides in length

30) Fill in the blank. Theorem 15-D: The shortest segment from a point to a line is a __________ line segment between the point and the line.

250 character(s) left
Your answer is too long.

31) Copy or print out the partial proof of Theorem 15-D shown below. State the number and the corresponding statement or reason. There are three missing parts of the proof.

250 character(s) left
Your answer is too long.

32) Fill in the blank. Theorem 15-E (Triangle Inequality Theorem): The sum of the lengths of any two sides of a triangle is __________ than the length of the third side.

250 character(s) left
Your answer is too long.

33) Will the three segments given below form a triangle? Explain why or why not.

4000 character(s) left
Your answer is too long.

Attachments

There are no attachments

Attach a File

34) Which set of lengths will form a triangle?

a.) 4, 1, 1

b.) 2, 9, 3

c.) 4, 5, 6

d.) 7, 3, 4

35) Fill in the blank. Theorem 15-F [Hinge Theorem (SAS Inequality)]: If two sides of a triangle are congruent to two sides of a second triangle and if the included angle on one triangle is greater than the included angle on the second triangle, then the third side of the first triangle is __________ than the third side of the second triangle.

250 character(s) left
Your answer is too long.

36) Which side is longer?

a.) JK

b.) MP

37) Study the information and figure given below. Which statement is true?

a.) MN = PO

b.) MN > PO

c.) MN < PO

38) Please explain how the Hinge Theorem could be used to solve the previous problem.

4000 character(s) left
Your answer is too long.

Attachments

There are no attachments

Attach a File

39) Fill in the blanks. Theorem 15-G (SSS Inequality Theorem): If two sides of a triangle are congruent to two sides of a second triangle, and if the third side of one triangle is greater than the third side of the second triangle, then the __________ between the two congruent sides in the first triangle is greater than the __________ between the two congruent sides in the second triangle.

250 character(s) left
Your answer is too long.

40) Which angle is greater in size?

a.) angle ABC

b.) angle DEF

41) Study the information and figure given below. Which statement is true?

a.) The measurement of angle UVT is equal to the measurement of angle UVW.

b.) The measurement of angle UVT is less than the measurement of angle UVW.

c.) The measurement of angle UVT is greater than the measurement of angle UVW.

42) Write an inequality to describe a solution for “t” in the figure below, and then solve for “t”.

250 character(s) left
Your answer is too long.

43) Draw a picture to illustrate the information given below, and then answer the following questions: a) What is the value of “x”? (b) What is the measure of angle AMB? (c) What is the measure of angle AMC? (d) Which side of the triangle is longer, AB or AC?

250 character(s) left
Your answer is too long.

44) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form.

No offline activities found

0 Hour(s) & 0 Minute(s)

If you are NOT required to complete Offline Activities for this course, please check the box below.

I do not have any Offline Activities for this unit.

Attachments

There are no attachments

Attach a File