Chapter 10 Part 1 Review

Chapter 10 Part 1 Review

Complete this review with a score of 100% in order to retake the Chapter 10 Part 2 test.

Point

A point has NO dimension and is represented by a dot.

Point B, E, C, D are all points on this plane

Line

A line has ONE dimension and is represented by a line with two arrowheads. It extends infinitely in each direction.

Through any TWO points there is exactly ONE line.

You can use any TWO points to name a line.

Line AB, Line CD, Line BE

Plane

A plane has TWO dimensions and is represented by a shape that looks like a floor or a wall.

Through any three points not on the same line, there is exactly one plane. You can use three points that are not all on the same line to name a plane. (non-coplanar)

Multiple Choice

Name two points collinear to Point K

• H & M

• J & L

• N & J

• M & L

Multiple Choice

Give another name for line k.

• Line BC

• Line BCE

• Line ED

• Line k is the only name, there isn't another name.

Multiple Choice

What is the length of PR?

• 11

• 8

• 5

• 3

Multiple Choice

What is the length of AB?

• 14

• 9

• 5

• 4

Finding a Midpoint

The midpoint of a line segment is the point that divides the segment into two segments that have the same length. A line, ray, or other figure that passes through the midpoint of a segment is a segment bisector.

​

You can use the Midpoint Formula to find the midpoint of a segment on the coordinate plane.​

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Practice and

Problem Solving

A/B #5-6

​

Multiple Choice

Which of the following points is the midpoint of (2, 5) and (6, 13)?

• (4, 9)

• (3, 7)

• (5, 8)

• (7, 12)

Multiple Choice

The endpoints of segment CD are C (3, -5) and D (7, 9). Find the coordinates of the midpoint?

• (3, 5)

• (5, 2)

• (6,8)

Finding an endpoint

• Use the midpoint formula.

• Substitute in values and solve for the variable.

​Let's do the next question together

Multiple Choice

The midpoint M and one endpoint of segment GH is given. Find the coordinates of the other endpoint. G(5, -6) and M(4,3).

• (3, 12)

• (6, 4)

• (1, 2)

Multiple Choice

What formula is the distance formula?

Find the distance between the points (0,0) and (6,8).

To find the distance:

1. Plug in (6) for X₂ and (0) for X₁.

2. Plug in (0) for Y₂ and (0) for Y₁.

3. Simplify your answer to find d.

Find the distance between the points (-3,2) and (3,5).

1. Plug in (3) for X₂ and (-3) for X₁.

2. Plug in (5) for Y₂ and (2) for Y₁.

3. Simplify your answer to find d.

Note: Sometimes you will have to split your square roots to find a simpler answer.

Multiple Choice

Find the distance between the following points:

(1,4) & (4,0)

• 10

• 5

• 25

• 30

Multiple Choice

What is the distance between the two points?

• $$2\sqrt{10}$$

• 4

• $$4\sqrt{10}$$

• $$10\sqrt{2}$$

Perimeter: The distance AROUND a two-dimensional figure.

If the little person was to walk AROUND the rectangle...they would walk 21 ft, then 9 ft, then 21 ft, then 9 ft and be back where they started.

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So 21 ft + 9 ft + 21 ft + 9 ft = 60 ft

Multiple Choice

Find the AREA of this figure.

• 160 square feet

• 160 feet

• abcdefghijklmnopqr stuvwxyz

• 1600 feet

circumference = the distance around a circle​

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​Let's start with circumference

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area = the region enclosed by the circular boundary​

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​AREA of a circle

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Terms, Values, and Formulas to Remember

Fill in the Blanks

What is the circumference of the circle shown? Round your answer to the nearest tenths place.

Multiple Choice

What is the area of this circle?

• 1256.64

• 31.41

• 314.16

• 123.12

Multiple Choice

• 44.4 mm²

• 5.92 mm²

• 8.88 mm²

• 17.76 mm²

Fill in the Blanks

What is the perimeter of the figure?

​Classifying Polygons

Polygons are classified by their number of sides. You can see in the table to the right the different names of each polygon. Polygons with more than ten sides are usually called n-gons where n is the number of sides it has (for example, a 27 sided polygon is called a 27-gon). ​12-sided polygons are called dodecagons.

​Convex and Concave

​Convex polygons have no sides that contain a point on the interior of the polygon.

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​Concave polygons are nonconvex polygons.

Multiple Choice

Is the polygon concave or convex?

• concave

• convex

Multiple Choice

Both of these figures are--

• Pentagons

• Octagons

• Nonagons

• Quadrilaterals

Multiple Choice

If the  $$m\angle7\ =\ 115\degree,$$  find the measure of  $$\angle2.$$  

• $$115\degree$$  

• $$65\degree$$  

• $$180\degree$$  

• Cannot be determined

Multiple Choice

If angle P measures 60 degrees, what is the measure of angle C?

• 60 degrees

• 30 degrees

• 120 degrees

Proofs Review

Open Ended

This is an example of a completed proof. It is proving that Vertical Angles are congruent.

What do you notice?

Open Ended

This is an example of a completed proof. It is proving that Vertical Angles are congruent.

What do you wonder?

Open Ended

Let's try one.....What do you notice?

Open Ended

What do you wonder?

Open Ended

What do you think should go as the first Statement? How do you know?

Open Ended

What do you think should go as the second Statement? How do you know?

Open Ended

What do you think should go as the third Reason? How do you know?

Open Ended

What do you think should go as the last statement? How do you know?

Open Ended

What do you think should go as the last Reason? Hint: We can't use "Alternate Interior Angles" as a Reason because that is what we are proving.

Open Ended

What do you notice?

What do you wonder?

Open Ended

What do you think we should do to prove that

<1+<2 = 180? Hint: We can use any reason to prove it as long as we don't use "Same Side Interior Angles" as a reason.