Review of Geometry
Prepared by Title V Staff:Daniel Judge, Instructor
Ken Saita, Program Specialist
East Los Angeles College
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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 3
Region 2
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These regions are referred to as:
Interior Region – Region bounded by both lines.
Exterior Region – The remaining outside regions.
exterior
exterior
interior
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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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l1
l2
AB
CD
Adjacent Angles – Angles that share a common vertex and a common side between them.
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l1
l2
AB
CD
Note:B and C are adjacent (neighbors)C and D are adjacent (neighbors)D and A are adjacent (neighbors)
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l1
l2
AB
CD
Vertical Angles – The pairs of non-adjacent angles formed by the intersection of two lines.
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Q: What’s special about vertical angles?Answer – They have the same measure. (they are congruent)
l1
l2
110°
110°70°70°
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Fact – When you intersect two lines at a point
l1
l2
A
CBD
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
l2
A
CBD
A and B are supplementary angles.
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Revisiting the transversal, copy this picture in your notebook.
l1
l2
Note: (l1 l2)
A BC D
HGE F
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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.
l1
l2
A BC D
HGE F
Interior Interior
Exterior
ExteriorEXITTOPICS BACK NEXT
Q: Which angles are adjacent?Q: Which angles are vertical?Q: Which angles are supplementary?
l1
l2
A BC D
HGE F
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Yes! If we could slide l2 up to l1, wewould be looking at the following picture.
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l1
l2
AC
BD
FEG 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.
l1
l2
120°C
BD
FEG H
l1 l2
What are the measures of the other angles?
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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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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 angles are 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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The sum of the interior angles of any triangle measures 180°
A
B C
That is, A + B + C = 180°
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That is, B + A + C = 180°
A
B C
A
B C
Note – The order in which we add doesn’t matter.
B C
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End of Review of Geometry
Title V East Los Angeles College
1301 Avenida Cesar ChavezMonterey Park, CA 91754
Phone: (323) 265-8784
Email Us At:[email protected]
Our Website:http://www.matematicamente.org
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