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MTH 214 Week 2 Study Plan

This assignment allows you to obtain the necessary practice to fully comprehend the weekly learning objectives, and prepare you to be successful on the weekly checkpoint and final.

Complete the MyMathLab® Study Plan for this week’s Checkpoint.

1. Click the Practice/Simulation/Homework/Game tab.
2. Click External Content Launch to access MyMathLab®.
3. Click Homework and Tests in MyMathLab® on the top left corner of the screen.
4. Click Study Plan for the weekly Checkpoint.
5. Click the green Practice button next to the first unmastered objective.
6. Complete the practice problems until you feel ready to take a quiz.
7. Click the Close button. Return to the Study Plan for the weekly Checkpoint.
8. Click the Quiz Me button.
9. Correctly answer the questions to earn the Mastery Point. There may be 2 or 3 questions per Quiz Me.

   1. If you do not correctly answer the questions in the Quiz Me, you must return to Practice and successfully complete at least 1 practice problem before you can retake the Quiz Me.
   2. You can follow this process and attempt each Quiz Me as often as necessary.

10. After earning the Mastery Point for the first objective, continue working in the Study Plan using the same process described above until you have earned all Mastery Points for the week.

Note: You must earn at least 80% of the Mastery Points this week before moving on to the Checkpoint. It is highly recommended you earn 100% of the Mastery Points before moving on to the Checkpoint.

Find the measure of the angle marked x in each of the following triangles.

(a)                             (b)                   (c)                                    (d)

In triangle a, two of the interior angles measure 57 degrees and x. The exterior angle at the third vertex measures 137 degrees. In triangle b, one of the interior angles is marked with a small square. The remaining angles measure x and 67 degrees. In triangle c, two of the interior angles measure 59 degrees and x. The exterior angle at the third vertex measures 2 x. In triangle d, the top angle is marked with a small square and the angle at the bottom left measures x. A line segment extends from the top vertex to the bottom side and is perpendicular to the bottom side, dividing the triangle into two smaller triangles. In the triangle on the right, the angle at the top left measures 68 degrees.

57 degrees57°

137 degrees137°

xx

67 degrees67°

xx

59 degrees59°

2 x2x

xx

xx

68 degrees68°

(a) Find the measure of x in figure a.

xequals=

8080degrees°

(b) Find the measure of x in figure b.

xequals=

2323degrees°

(c) Find the measure of x in figure c.

xequals=

5959degrees°

(d) Find the measure of x in figure d.

xequals=

6868degrees

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A triangle has two sides of length 10 cm and 14 cm. What can you say about the length of the third side?

Choose the correct answer below.

A.

The third side must be less than 24 cm and greater than 4 cm.

The third side must be less than 140 cm.

C.

The third side must be greater than 24 cm and less than 140 cm.

D.

The third side must be greater than 4 cm.

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How does this fifth grade common core type geometry question challenge a student’s understanding of shapes?

Choose the correct answer below.

A.

Students must understand how to compose, decompose, and transform shapes.

B.

Students must be able to classify three-dimensional figures based on their properties.

C.

Students must create conjectures based on the properties of the shapes.

D.

Students must know shapes and their properties, as well as what subcategories the shapes belong to based on their properties.

The figure below is a rectangular box in which EFGH and ABCD are rectangles and BF overbarBF is perpendicular to planes EFGH and ABCD.

Use the figure to complete parts a through d.

A rectangular box has rectangular bases A B C D and E F G H. The following edges are perpendicular to the bases: A E; B F; C G; D H. Rectangle B D H F is inside the rectangular box.

H

G

F

E

A

B

C

D

a. What is the intersection of ModifyingAbove CG with left right arrowCG and plane ABCABC?

b. Which pair of planes are perpendicular?

c. Which lines are perpendicular to plane CDGCDG?

d. What is the measure of the dihedral angle Upper D dash GH dash Upper FD-GH-F?

a. What is the intersection of ModifyingAbove CG with left right arrowCG and plane ABCABC?

A.

empty set∅

B.

{Upper BB}

C.

{Upper CC}

Your answer is correct.D.

{Upper FF}

b. Which pair of planes are perpendicular?

A.

ABC and EFG

B.

ADE and BCF

C.

ABEABE and EFGEFG

Your answer is correct.D.

ABE and CDG

c. Which lines are perpendicular to plane CDGCDG? Select all that apply.

A.

ModifyingAbove CD with left right arrowCD

B.

ModifyingAbove EF with left right arrowEF

C.

ModifyingAbove AD with left right arrowAD

Your answer is correct.D.

ModifyingAbove EH with left right arrowEH

Your answer is correct.

d. What is the measure of the dihedral angle Upper D dash GH dash Upper FD-GH-F?

9090degrees

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How does this sixth grade geometry common core type question meet the goals behind the common core standards?

Choose the correct answer below.

A.

It assesses students’ ability to transform shapes.

B.

It assesses students’ understanding of the properties of cubes, as well as their ability to find multiple ways to create a cube.

It assesses students’ ability to classify three-dimensional shapes.

D.

It assesses students’ ability to find relationships between different three-dimensional shapes.

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A student claims that all squares are congruent to each other. How do you respond?

Choose the correct answer below.

A.

The student is correct. A square has four sides of the same length and four angles of the same measure, so all squares are congruent.

B.

The student is correct. All squares have four 90degrees° angles, so their angles are congruent, meaning that all squares must be congruent.

C.

The student is incorrect. Although all squares have four congruent 90degrees° angles, any congruent squares must also have the same side lengths, which is not true for all squares.

The student is incorrect because not all squares have congruent angles.

Identify a physical object to represent each of the following.

a. Parallel lines

b. Parallel planes

c. Skew lines

d. A right angle

a. Choose the correct answer below.

A.

The opposite edges of the side of a table

Your answer is correct.B.

The intersection of the floor and two adjacent walls of a room

C.

Two adjacent edges of the side of a table

D.

The covers of a book

b. Choose the correct answer below.

A.

The opposite edges of the side of a table

B.

A horizontal and vertical edge of a cube that do not share a vertex

C.

The covers of a book

Two adjacent walls in a room

c. Choose the correct answer below.

A.

The covers of a book

B.

The intersection of the floor and two opposite walls of a room

C.

The intersection of the floor and two adjacent walls of a room

D.

A horizontal and vertical edge of a cube that do not share a vertex

d. Choose the correct answer below.

A.

The intersection of the floor and two opposite walls of a room

B.

The opposite edges of the side of a table

C.

A horizontal and vertical edge of a cube that do not share a vertex

D.

The edge of a table and one leg of that table meeting that edge

Classify each of the following as true or false.

a. If a rhombus is a square comma it must also be a rectangleIf a rhombus is a square, it must also be a rectangle.

b. All squares are trapezoidsAll squares are trapezoids.

a. Is the statement “If a rhombus is a square comma it must also be a rectangleIf a rhombus is a square, it must also be a rectangle” true or false? Choose the correct answer below.

FalseFalse

TrueTrue

Your answer is correct.

b. Is the statement “All squares are trapezoidsAll squares are trapezoids” true or false? Choose the correct answer below.

TrueTrue

Your answer is correct.

False

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Maggie claims that to make the measure of an angle greater, you just extend the rays. How do you respond?

Choose the correct answer below.

A.

Maggie is correct.

B.

Maggie is incorrect. You cannot extend the rays of an angle.

C.

Maggie is incorrect. Extending the rays decreases the angle measure.

D.

Maggie is incorrect. Extending the rays does not change the angle measure.

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One student says, “My sister’s high school geometry book talked about equal angles. Why don’t we use the term “equal angles” instead of “congruent angles?” How do you reply?

Choose the correct answer below.

A.

There is no difference between “equal angles” and “congruent angles.” Either wording can be used.

B.

Congruent angles only make sense when talking about a polygon. Open angles cannot be congruent.

C.

Since an angle is a set of points determined by two rays with the same endpoint, to say that two angles are equal implies that the two sets of points determining the angles are equal. The only way this can happen is if the two angles are actually the same angle.

“Equal angles” require the addition of two angles while “congruent angles” do not.

Identify each of the following triangles as acute, obtuse, right, or equiangular. (There may be more than one term that applies to these triangles.)

a. Choose the correct classification below.

A.

acuteacute

B.

acute and equiangularacute and equiangular

Your answer is correct.C.

obtuseobtuse

D.

rightright

b. Choose the correct classification below.

A.

rightright

B.

obtuseobtuse

C.

acuteacute

Your answer is correct.D.

acute and equiangularacute and equiangular

c. Choose the correct classification below.

A.

rightright

Your answer is correct.B.

acute and equiangularacute and equiangular

C.

obtuseobtuse

D.

acute

Classify the polygon shown to the right.

Choose the correct classification below.

A.

ParallelogramParallelogram but not squaresquare

Your answer is correct.B.

TrapezoidTrapezoid but not rectanglerectangle

C.

RhombusRhombus but not kitekite

D.

KiteKite but not trapezoid

How does this seventh grade common core type question challenge a student’s understanding of triangles more so than a traditional triangle question?

Choose the correct answer below.

A.

Students must find all of the different ways to create a triangle based on the criteria.

Students must know the definition of the different types of triangles.

C.

Students must be able to use mathematical tools to measure angles of multiple triangles.

D.

Students must be able to classify triangles.

Determine if the figure to the right has (a) line symmetry, (b) rotational symmetry, and/or (c) point symmetry.

A rectangle has two horizontal and two vertical sides. Centered above the rectangle is a circle. Centered below the rectangle is another circle. The distance from the bottom of the upper circle to the top of the rectangle is the same as the distance from the top of the lower circle to the bottom of the rectangle.

Does the figure have line symmetry?

YesYes

Your answer is correct.

NoNo

Does the figure have rotational symmetry?

NoNo

YesYes

Your answer is correct.

Does the figure have point symmetry?

NoNo

YesYes

Identify and sketch the lines of symmetry for the following figures, if any exist.

Determine the number of lines of symmetry, if any, in the figure. Sketch the lines of symmetry for each figure, if they exist. Select the correct answer below and fill in the answer box to complete your choice.

(Type a whole number.)

A.

A triangle has a horizontal bottom side, a vertical side, a third side that falls from left to right. It is indicated that there are no lines of symmetry.

No lines of symmetry

There is/are

00 line(s) of symmetry.

Your answer is correct.B.

A triangle has a horizontal bottom side, a vertical side, a third side that falls from left to right. Three dashed, double-ended arrows run through parts of the triangle. The first arrow falls from left to right, intersecting the top of the vertical side and the right of the horizontal side. The second arrow runs horizontal through the middle of the triangle. The third arrows run vertical, intersecting the left side of the falling side and the left side of the horizontal side.

There is/are

nothing line(s) of symmetry.

C.

A triangle has a horizontal bottom side, a vertical side, a third side that falls from left to right. Three dashed, double-ended arrows run through parts of the triangle. The first arrow falls from left to right, intersecting the middle of the vertical side and the bottom right vertex. The second arrow falls from left to right, intersecting the top left vertex and the middle of the horizontal side. The third arrow rises from left to right, intersecting the bottom left vertex and the middle of the falling side.

There is/are

nothing line(s) of symmetry.

Determine the number of lines of symmetry, if any, in the figure. Sketch the lines of symmetry for each figure, if they exist. Select the correct answer below and fill in the answer box to complete your choice.

(Type a whole number.)

A.

An irregular hexagon. The top and bottom sides are shorter than the rest of the sides. It is indicated that there are no lines of symmetry.

No lines of symmetry

There is/are

nothing line(s) of symmetry.

B.

An irregular hexagon. The top and bottom sides are shorter than the rest of the sides. Four dashed, double-ended arrows run through parts of the hexagon. The first arrow runs vertically, intersecting the middle of the top and bottom sides. The second arrow runs horizontally, intersecting the left and right vertices. The third arrow falls from left to right, intersecting the top left and bottom right sides. The fourth arrow rises from left to right, intersecting the bottom left and top right sides.

There is/are

nothing line(s) of symmetry.

C.

An irregular hexagon. The top and bottom sides are shorter than the rest of the sides. Two dashed, double-ended arrows run through parts of the hexagon. The first arrow runs vertically, intersecting the middle of the top and bottom sides. The second arrow runs horizontally, intersecting the left and right vertices.

There is/are

22 line(s) of symmetry.