Geometry Foundations Exam Part One

The big idea Identify angle pairs first, then use congruent, complementary, or supplementary relationships to solve.

Read one intersection

Vertical angles are opposite and congruent. Adjacent angles share a side. A linear pair is adjacent and forms a straight line, so the measures add to 180°.

Complementary angles add to 90°. Supplementary angles add to 180°.

Ask in order: opposite or touching? Then equal, 90°, or 180°?

Two intersecting lines forming four numbered angles — Opposite corners are vertical; neighbors along a line form a linear pair.

Name transversal pairs

Corresponding: same corner at each intersection. Alternate interior: inside the lines on opposite sides. Alternate exterior: outside the lines on opposite sides. Same-side interior: inside the lines on the same side.

Find inside or outside first. Then decide same side or opposite side.

Two parallel lines cut by a transversal with eight angle positions — Position determines the angle-pair name.

Use the parallel-line results

If the lines are parallel, corresponding, alternate interior, and alternate exterior angles are congruent. Same-side interior angles are supplementary.

Memory check: three relationships give equal measures; the inside-and-same-side pair gives 180°.

Alternate interior angles highlighted on parallel lines — Alternate interior angles are congruent.

Same-side interior angles highlighted on parallel lines — Same-side interior angles add to 180 degrees.

Turn the relationship into an equation

Suppose same-side interior angles measure (6x + 12)° and (4x + 18)°. They are supplementary:

(6x+12)+(4x+18)=180

Combine like terms: 10x + 30 = 180. Subtract 30: 10x = 150. Divide by 10: x = 15. Check by substituting: 102° + 78° = 180°.

Same-side interior angles on two parallel lines — The geometry relationship supplies the equation; algebra solves it.

Check Part 3

Name the pair before deciding whether the measures are equal or total 180°.

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