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Chapter IV review
Textbook: pp. 92–93
GoalReview Chapter IV on parallel lines.
New words
parallel axiom · parallellik aksiomasitests for parallel lines · parallellik alomatlariconverse theorem · teskari teoremacounterexample · kontrmisol
Explanation
Review: parallel lines lie in one plane and do not meet. Axiom: through a point exactly one parallel to a line can be drawn. Tests: equal alternate (or corresponding) angles, or same-side interior angles adding to 180°, make the lines parallel. Converse theorems: if the lines are parallel, alternate and corresponding angles are equal and same-side interior angles add to 180°. A converse is not always true, so a proof or a counterexample is needed. In a problem, first decide whether a ∥ b is given or must be proved.
Worked examples
Same-side interior angles 112° and 68°: 112° + 68° = 180° ⇒ the lines are parallel.
a ∥ b and corresponding angles 2x and x + 35°: 2x = x + 35°, x = 35°, the angles are 70°.
Class activity
“Chapter relay”: two teams take turns naming a test, axiom or theorem; repeated ones score nothing.
Practice
1
a ∥ b. Corresponding angles are 3x and x + 60°. x = ?
30
2
Alternate interior angles are 76° and 76°. If one same-side interior angle is 76°, find the other (degrees).
104
3
Which corollary says “corresponding angles equal ⇒ lines parallel”?
Corollary 1
4
Why do same-side interior angles of parallel lines add up to 180°?
The alternate interior angles are equal and one is adjacent to the same-side angle, so the sum is 180°.