Use properties of parallel lines cut by a transversal to find unknown angle measures

Lines that are cut by a transversal may or may not be parallel

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QUESTION OF
Views #: 538
Questions #: 11
Time: 5 minutes
Pass Score: 80.0%
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Corresponding angles property

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volume_mute

If two parallel lines are cut by a transversal, each pair of corresponding angles are congruent

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Explanation

In the figure below

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If \(l_1 \parallel l_2\), then

  • ∠ 1 ≅ (1)
  • ∠ 3 ≅ (2)
  • ∠ 2 ≅ (3)
  • ∠ 4 ≅ (4)
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∠ 8
∠ 5
∠ 6
∠ 7
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Alternate interior angles property

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If two parallel lines are cut by a transversal, alternate interior angles are congruent

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Explanation

In the following figure

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if \(l_1 \parallel l_2 \) then

  • ∠3 ≅ (1)
  • ∠4 ≅ (2)
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∠6
∠5
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Interior angles property

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In the figure below, If \(l_1 \parallel l_2\) then

  • ∠3 is supplementary to (1)
  • ∠4 is supplementary to (2)
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∠6
∠5
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If a transversal is perpendicular to one of the two parallel lines, it is also perpendicular to the other line

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If two lines are parallel to a third line, the are not necessarily parallel to each other

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Refer to the below figure

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If \(l_1 \parallel l_2 \) and m(∠3) = 120o, find the measures of the other seven angles that are labelled.

  1. m(∠1) = (1)
  2. m(∠2) = (2)
  3. m(∠4) = (3)
  4. m(∠5) = (4)
  5. m(∠6) = (5)
  6. m(∠7) = (6)
  7. m(∠8) = (7)
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Explanation

Refer to the figure below

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volume_mute

if \(\overline{AB} \parallel \overline{DE} \), which pairs of angles are congruent?

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In the figure below

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\(l_1 \parallel l_2 \).  Find \(x\)

\(x\) = (1)

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In the figure below

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\(l_1 \parallel l_2\)

  1. Find \(x\)
  2. Find the measures of both angles labelled in the figure

\(x\) = (1)

m(3x + 20o) = (2)

m(3x - 80o) = (3)

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Keywords
Year 10