Geometry · Unit 3
Name corresponding, alternate interior, alternate exterior, consecutive interior, vertical, and linear pairs.
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Transversal
A transversal is a line that crosses two or more other lines. The other lines do not have to be parallel.
Example: line t in the diagram crosses lines a and b.
The eight angles
Corresponding: 1 and 5, 2 and 6, 4 and 8, 3 and 7 (same corner at each intersection).
Alternate interior: 4 and 6, 3 and 5 (inside, opposite sides of t).
Alternate exterior: 1 and 7, 2 and 8 (outside, opposite sides of t).
Consecutive interior: 4 and 5, 3 and 6 (inside, same side of t).
Always true
Vertical angles are congruent. Example: m∠1 = m∠3.
A linear pair is supplementary. Example: m∠1 + m∠2 = 180°.
True when the lines are parallel
If a ∥ b, corresponding angles are congruent, alternate interior angles are congruent, and consecutive interior angles are supplementary.
Example: if a ∥ b and m∠1 = 70°, then m∠5 = 70° (corresponding).
Name the pair from the numbered diagram.
Corresponding angles sit in the same corner at each intersection.
One pair is ∠1 and ∠5.
Answer: ∠1 and ∠5 (or 2 and 6, 4 and 8, 3 and 7)
A linear pair is two adjacent angles that make a straight line.
∠1 and ∠2 are a linear pair.
Answer: ∠1 and ∠2 (or any two that share a ray and sit on a line)
Outside the two lines, on opposite sides of the transversal.
∠1 and ∠7.
Answer: ∠1 and ∠7 (or 2 and 8)
Vertical angles are opposite each other at an intersection.
∠1 and ∠3.
Answer: ∠1 and ∠3 (or 2 and 4, 5 and 7, 6 and 8)
Inside the two lines, on the same side of the transversal.
∠4 and ∠5.
Answer: ∠4 and ∠5 (or 3 and 6)
No. A transversal is any line that crosses two or more lines.
The special congruent and supplementary relationships need parallel lines. The names (corresponding, alternate interior, and so on) still apply even when the lines are not parallel.
Answer: no
More than one pair, or a name plus a reason.
Interior means between a and b. Alternate means opposite sides of t.
∠4 and ∠6; ∠3 and ∠5.
Answer: ∠4 & ∠6; ∠3 & ∠5
∠4 is the lower-left angle at the top intersection.
The same corner at the bottom intersection is ∠8.
Answer: ∠8
∠2 and ∠8
Answer: ∠2 and ∠8
Vertical angles are always congruent.
Corresponding and alternate interior need a ∥ b to be congruent.
Answer: only vertical angles
They are adjacent and sit on line a, so they are a linear pair.
Answer: linear pair
Yes. The name describes position, not measure.
They are congruent only when the lines are parallel.
Answer: yes; they just are not congruent unless the lines are parallel
Use the names to sort several pairs at once.
(1, 5) corresponding
(4, 6) alternate interior
(2, 4) vertical
(3, 6) consecutive interior
(1, 3) vertical
Answer: corresponding; alt. interior; vertical; consecutive interior; vertical
Corresponding angles are congruent when the two lines are parallel.
Without parallel lines, corresponding angles can have different measures.
Answer: congruent only if the lines are parallel
Corresponding: ∠7
Alternate interior: ∠5
Vertical: ∠1
Answer: corresponding ∠7; alt. interior ∠5; vertical ∠1
Vertical to ∠4 is ∠2, so m∠2 = 110°.
Linear pair with ∠4: m∠1 = 70° and m∠3 = 70°.
You cannot find 5, 6, 7, or 8 without parallel lines or more information.
Answer: m∠2 = 110°; m∠1 = m∠3 = 70°
Both angles are between a and b (interior).
They are on the same side of t, not opposite sides.
Same side − consecutive. Opposite sides − alternate.
Answer: same side of the transversal
Corresponding: (1, 5), (2, 6), (4, 8), (3, 7)
Alternate interior: (4, 6), (3, 5)
Consecutive interior: (4, 5), (3, 6)
Answer: (1,5) (2,6) (4,8) (3,7); (4,6) (3,5); (4,5) (3,6)
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