STAIR: Project DevelopmentSTAIR: Project Development

Geometry Review & ExercisesGeometry Review & Exercises

Presented by Joys SimonsPresented by Joys Simons

Lines Introduction

Lines Questions

Answers to Lines

Reminder - Lines

Angles Introduction

Angles Questions

Answers to Angles

Reminder - Angles

Circles Introduction

Circles Questions

Answers to Circles

Reminder - Circles

Lines Quiz

Angles Quiz

Circles Quiz

Lines Q. Review

Angles Q. Review

Circles Q. Review

In geometry, a basic building block is the line, which is understood to be a “straight” line. It is also understood that lines are infinite in length. In the figure below, A and B are points on line .

• What is it called? (That part of line from A to B, including the endpoints A and B )

• Which is ? in length?

. .

That part of line from A to B, including the endpoints A and B, is called a line segment, which is finite in length.

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Sometimes the notation “AB” denotes line segment AB and sometimes it denotes the length of line segment AB. The exact meaning of the notation can be determined from the context.

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Lines 1 and 2 , shown below, intersect at point P. Whenever two lines intersect at a single

point, they form four angles.

. .

• What do the opposite angles called?

• What is the sum of the measures of the four angles?

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Opposite angles, called vertical angles, are the same size, i.e., have equal measure. Thus, APC and DPB have equal measure, and APD and CPB also have equal measure. The sum of the measures of the four angles is 360°.

An angle that measures 90 is called a right angle, and an angle that measures 180 is called a straight angle.

The set of all points in a plane that are a given distance r from a fixed point O is called a circle. The point O is called the center of the circle, and the distance r is called the radius of the circle. Also, any line segment connecting point O to a point on the circle is called a radius.

. .

• What is it called for any line segment that has its endpoints on a circle, such as PQ below?

• What is it called for What is it called for any chord that passes through the center of a circle?

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Any line segment that has its endpoints on a circle, such as PQ below, is called a chord. Any chord that passes through the center of a circle is called a diameter.

. .

the diameter of a circle is always equal to twice its radius. The distance around a circle is called its circumference. In any circle, the ratio of the circumference c to the diameter d is a fixed constant, denoted by the Greek letter Л.

. .

Lines l and m below are parallel. Find the values of x and y.

x=57, y=138x=57, y=138 X=50, y=140 x=55, y=145X=50, y=140 x=55, y=145

A B C

In the figure below, AC = BC. Find the values of x and y.

x=65, y=120x=65, y=120 X=70. y=125 x=75, y=130X=70. y=125 x=75, y=130

A B C

The figure below shows two concentric circles each with center O. If the larger circle has radius 12 and the smaller circle has radius 8, find the

area of the shaded region.

The area = 78 The area = 78 ЛЛ The area = 75 The area = 75 ЛЛ The area = 80 The area = 80 ЛЛ

A C B

Back to Lines QuizBack to Angles QuizBack to Circles Quiz

Back to Lines QuizBack to Angles QuizBack to Circles Quiz

Geometry review & Exercises

Geometry Review Geometry Exercises

Lines Angles Circles Lines Angles Circles

Quiz & Interaction will be placed here

Lines l and m below are parallel. Find the values of x and y.

From our Lines introduction chapter, we knew when two lines are From our Lines introduction chapter, we knew when two lines are parallel, parallel,

the angles on the same side will be equal; we should also the angles on the same side will be equal; we should also remember, the remember, the

opposite angles are equal; since the opposite angle of 57° has opposite angles are equal; since the opposite angle of 57° has already already

provided to us, that’s why provided to us, that’s why the x = 57the x = 57. On the other hand, we . On the other hand, we knew that knew that

the straight angle = 180° and the opposite angle is 42° (It is the the straight angle = 180° and the opposite angle is 42° (It is the provided provided

information.) So information.) So y = 180 - 42 = 138y = 180 - 42 = 138.. Please contact me at chaosimo@msu.edu if you need help.Please contact me at chaosimo@msu.edu if you need help.

In the figure below, AC = BC. Find the values of x and y.

From our Angles introduction chapter, we knew that if a triangle has From our Angles introduction chapter, we knew that if a triangle has two sides two sides

of equal length, then the measures of the angles opposite the two of equal length, then the measures of the angles opposite the two sides are sides are

equal. The information of AC = BC was provided, and we knew the equal. The information of AC = BC was provided, and we knew the

information of 125°, so information of 125°, so 180° – 125° = 55°180° – 125° = 55° (That means both (That means both Angles BAC Angles BAC

and ABC = 55°.) Thus, and ABC = 55°.) Thus, X = 180 – 55 – 55 = 70; X = 180 – 55 – 55 = 70;

Y = 180 – 55 = 125.Y = 180 – 55 = 125.

Please contact me at chaosimo@msu.edu if you need help.Please contact me at chaosimo@msu.edu if you need help.

The figure below shows two concentric circles each with center O. If the larger circle has radius 12 and the smaller circle has radius 8, find the area of the shaded region.

From our Circles introduction chapter, we knew the area = radiusFrom our Circles introduction chapter, we knew the area = radius² ² ЛЛ. Thus, . Thus,

the area of the larger circle = the area of the larger circle = 12² 12² ЛЛ = 144 = 144 ЛЛ ; and the area of the ; and the area of the smaller smaller

circle = circle = 8² 8² ЛЛ = 64 = 64 ЛЛ; so ; so the area of the shaded region should the area of the shaded region should be: be:

144 144 ЛЛ - 64 - 64 ЛЛ = 80 = 80 ЛЛ.. Please contact me at chaosimo@msu.edu if you need help.Please contact me at chaosimo@msu.edu if you need help.