Section 5'4 Conditions for Parallel Lines

1

• Section 5.4 Conditions for Parallel Lines
• Objective Apply the converses of theorems about
  parallel lines and transversals in proofs.
• Write the converse of each statement. Is the
  original statement true? The converse?
• If it rains today, we will stay inside.
• If a quad. Is a square, then it is a rhombus.
• Converse of the Corresponding Angles Postulate
• If two lines are intersected by a transversal
  and corresponding angles are congruent, then the
  lines are parallel.

If ?1 ? ?2, Then k m.
1
2
k
m
2

• How would you use the Converse of the
  Corresponding Angles Postulate to find the value
  of x that will allow you to prove that WXYZ is a
  trapezoid.

X
Y
(9x 25)
(4x 15)
Z
W
B
3

• Converse of the Alternate Interior Angles Theorem
• 5. Converse of the Same-Side Interior Angles
  Theorem

4

• 6. Prove that if two sides of a quadrilateral are
  parallel, and one pair of opposite angles are
  congruent, then the quadrilateral is a
  parallelogram.