unit 6: geometry lesson one: angle properties of parallel lines learning goals i can determine the...
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Unit 6: Geometry
Lesson One: Angle Properties of Parallel Lines
Learning Goals
I can determine the measure of angles using angle relationships involving triangles and parallel lines.
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Unit 6: Geometry
Lesson One: Angle Properties of Parallel Lines
Vocabulary:Parallel lines – two or more lines that run side by side but never
cross paths. Transversal – A line that intersects two or more parallel lines. Hatch Mark (or Tick Mark) – a mark on two or more sides of a
geometric shape to indicate the sides are equal lengths.
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The C-Pattern Rule/Co-Interior AnglesCo-interior angles have a sum of 180. They are between the parallel lines on the same side of the transversal. They form a C-Pattern.
𝒙+𝒚=𝟏𝟖𝟎°
Lesson One: Angle Properties of Parallel Lines
Unit 6: Geometry
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Determine the value of x using the c-pattern rule.
Lesson One: Angle Properties of Parallel Lines
Unit 6: Geometry
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The F-Pattern Rule/Corresponding Angles
Corresponding angles are equal. They have the same position with respect to the transversal and the parallel lines. They form an F-Pattern.
x = z
Lesson One: Angle Properties of Parallel Lines
Unit 6: Geometry
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Determine the value of “x” using the F-Pattern Rule
Lesson One: Angle Properties of Parallel Lines
Unit 6: Geometry
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The Z-Pattern Rule/Alternate Angles
Alternate angles are equal. They are between the parallel lines on opposite sides of the transversal. They form a Z-Pattern.
w = x
Lesson One: Angle Properties of Parallel Lines
Unit 6: Geometry
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Use the Z-Pattern Rule to determine the value of “x”.
Lesson One: Angle Properties of Parallel Lines
Unit 6: Geometry
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The t-Pattern Rule/Supplementary AnglesSupplementary angles have a sum of 180 They are created when a line is intersected by another line. They form a T-Pattern.
x + y = 180
Lesson One: Angle Properties of Parallel Lines
Unit 6: Geometry
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Determine the value of “x” using the t-Pattern Rule
Lesson One: Angle Properties of Parallel Lines
Unit 6: Geometry
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Opposite angles are equal. They are created when any two lines intersect. They are diagonally across from each other and form an X-Pattern.
w = zAnd
y = x
Unit 6: Geometry
Lesson One: Angle Properties of Parallel Lines
The X-Pattern Rule/Opposite Angles
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Complementary AnglesComplementary angles have a sum of 90They are created when a right angle is divided into two smaller angles.
a + b = 90
Unit 6: Geometry
Lesson One: Angle Properties of Parallel Lines
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Unit 6: Geometry
Lesson One: Angle Properties of Parallel Lines
When a transversal intersects two lines, four sets of opposite angles are formed.
The angles in each pair are equal. When a transversal crosses a pair of
parallel lines it creates:
• 4 sets of opposite angles (X-pattern)• 2 sets of alternate angles (Z-Pattern)• 4 sets of corresponding angles (F-
Pattern)• 2 sets of co-interior angles (C-Pattern)
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Unit 6: Geometry
Lesson One: Angle Properties of Parallel Lines
Practice
Page 359 Q 1, 2, 3a, 6b, 7, 8, 10a, 11
Page 366 Q 8ab