Review of Geometry

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# Review of Geometry - PowerPoint PPT Presentation

Review of Geometry. Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles College. Click one of the buttons below or press the enter key. TOPICS. BACK. NEXT. EXIT. © 2002 East Los Angeles College. All rights reserved. Topics.

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## Review of Geometry

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### Review of Geometry

Prepared by Title V Staff:Daniel Judge, InstructorKen Saita, Program SpecialistEast Los Angeles College

Click one of the buttons below or press the enter key

TOPICS

BACK

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EXIT

Topics

Click on the topic that you wish to view . . .

LinesAnglesTriangles

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### Lines

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When a pair of lines are drawn, the portion of the plane where the lines do not intersect is divided into three distinct regions.

Region 1

Region 2

Region 3

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These regions are referred to as:

Interior Region – Region bounded by both lines.

Exterior Region – The remaining outside regions.

exterior

interior

exterior

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Parallel Lines – Lines that never intersect.

l1

l2

Notationl1 l2

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Transversal – A line that intersects two or more lines in different points.

l1

l2

Note:l1 is not parallel to l2(l1 l2)

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Transversal

l1

l2

Note: l1 is parallel to l2(l1 l2)

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### Angles

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Angles are formed when lines intersect.

l1

A

Note: (l1 l2)

D

B

C

l2

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A and B are said to be adjacent. (neighbors)

l1

A

D

B

C

l2

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Adjacent Angles – Angles that share a common vertex and a common side between them.

l1

A

D

B

C

l2

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l1

A

D

B

C

l2

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Vertical Angles – The pairs of non-adjacent angles formed by the intersection of two lines.

l1

A

D

B

C

l2

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l1

A

D

B

C

l2

Note:A and C are vertical anglesB and D are vertical angles

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Q: What’s special about vertical angles?

Answer – They have the same measure. (they are congruent)

l1

110°

70°

70°

110°

l2

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Fact – When you intersect two lines at a point

l1

A

D

B

C

l2

AC (congruent)B D (congruent)

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Two angles are said to be supplementary if their sum measures 180°.Adjacent angles formed by two intersecting lines are supplementary.

l1

A

D

B

C

l2

A and B are supplementary angles.

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l1

A

D

B

C

l2

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A

B

l1

C

D

Note: (l1 l2)

E

F

G

l2

H

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Angles in the interior region between the two lines are called interior angles. Angles in the exterior region are called exterior angles.

Exterior

A

B

l1

C

D

Interior

Interior

E

F

G

l2

H

Exterior

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A

B

l1

C

D

E

F

G

l2

H

Interior ExteriorCADBEGFH

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Q: Which angles are adjacent?Q: Which angles are vertical?Q: Which angles are supplementary?

A

B

l1

C

D

E

F

G

l2

H

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A

B

l1

C

D

E

F

l2

G

H

We know, A  DBCEHGF since they are all vertical angles.

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Yes! If we could slide l2 up to l1, wewould be looking at the following picture.

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A

B

l1

C

D

E

F

l2

G

H

This means the following is true:A and E have the same measure (congruent)B and F have the same measure (congruent)C and G have the same measure (congruent)D and H have the same measure (congruent)

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Having knowledge of one angle in the special transversal below, allows us to deduce the rest of the angles.

120°

B

l1

C

D

l1 l2

E

F

l2

G

H

What are the measures of the other angles?

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120°

60°

l1

60°

120°

l1 l2

120°

60°

l2

60°

120°

Why?

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### Triangles

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One of the most familiar geometric objects is the triangle. In fact, trigonometry is the study of triangles

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Triangles have two important properties 1. 3 sides 2. 3 interior angles

A

B

C

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Right Triangle —One interior angle ofthe triangle measures90° (has a right angle)

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Equilateral Triangle —1. All of the sides are congruent (have the samemeasure).

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Equiangular Triangle —1. All of the interior anglesare congruent (have the same measure).

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Note – Equiangulartriangles are alsoequilateral triangles. Equilateral triangles are also equiangular triangles.

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Isosceles Triangle —1. Two of the interior angles of the triangle are congruent (havethe same measure).2. Two of the sidesare congruent.

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A

B

C

That is, A + B + C = 180°

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Why?

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Solution--

A

A

B

C

B

C

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Fill in the remaining angles.

A

A

B

C

B

C

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Solution--

A

B

C

A

B

C

B

C

Do you notice anything?

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That is, B + A + C = 180°

A

B

C

A

B

C

B

C

Note – The order in which we add doesn’t matter.

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A

B

C

A + B + C = 180°(This is true for any triangle)

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End of Review of Geometry

Title V East Los Angeles College1301 Avenida Cesar ChavezMonterey Park, CA 91754Phone: (323) 265-8784Email Us At:menteprog@hotmail.comOur Website:http://www.matematicamente.org

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