Proof of Theorem for Quadrilateral Properties
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Questions and Answers

What is the relationship between the angles ∠A and ∠D in parallelogram ABCD?

  • They are vertical angles
  • They are congruent
  • They are supplementary (correct)
  • They are complementary
  • If m∠D = 53°, what is the measure of angle ∠C in parallelogram ABCD?

  • 107°
  • 143°
  • 73°
  • 127° (correct)
  • What can be concluded about the relationship between the opposite angles ∠B and ∠D in parallelogram ABCD?

  • They are vertical angles
  • They are supplementary
  • They are congruent (correct)
  • They are complementary
  • If m∠A = 110°, what is the measure of angle ∠C in parallelogram ABCD?

    <p>110°</p> Signup and view all the answers

    What is true about the relationship between ∠A and ∠B in a parallelogram?

    <p>They are equal</p> Signup and view all the answers

    Which property of the proportion does 𝑎+𝑏 𝑏 = represent?

    <p>Transitive Property</p> Signup and view all the answers

    What is the correct value of 𝒙 that makes the statement 𝒙 = 27 true?

    <p>81</p> Signup and view all the answers

    If ⃡𝐴𝐵 is parallel to ⃡𝑌𝑍 and intersects ̅̅̅̅ 𝑋𝑌 and ̅̅̅̅ 𝑋𝑍 at A and B, which ratio equals 𝐴𝑌 by the Triangle Proportionality Theorem?

    <p>𝐴𝐵 / 𝐵𝑍</p> Signup and view all the answers

    Which of the following ratios does not show a property of the proportion?

    <p>rac{a}{c} imes rac{b}{d} = 18</p> Signup and view all the answers

    If parallel lines cut congruent segments on one transversal, what property holds true for the corresponding angles?

    <p>Corresponding Angles Postulate</p> Signup and view all the answers

    What does the Triangle Angle Bisector Theorem state about a line bisecting an angle of a triangle?

    <p>It divides the opposite sides proportionally.</p> Signup and view all the answers

    What postulate is used to show that angles ∠𝐵𝑌𝐶 and ∠𝑍𝑌𝐷 are congruent?

    <p>Vertical Angle Theorem</p> Signup and view all the answers

    In the context of the text, why is it mentioned that Y is the midpoint of side ̅𝐵𝑍?

    <p>Because Y divides side ̅𝐶𝐷 into two equal segments.</p> Signup and view all the answers

    Why does the text mention that ̅𝐷𝑍 ≅ ̅𝐵𝐶?

    <p>Due to CPCTC.</p> Signup and view all the answers

    Why is it mentioned that ̅𝑋𝑌 ̅̅̅̅ ∥ ̅̅̅̅ in the context of the text?

    <p>Because of the definition of midline of a trapezoid.</p> Signup and view all the answers

    What must be true about the length of ̅X𝑌 in relation to the other sides of triangle ABZ?

    <p>$2XY = AZ$</p> Signup and view all the answers

    What does the statement 'ZD = BC' signify in the context provided?

    <p>$∆BDC$ is an isosceles triangle.</p> Signup and view all the answers

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