Unit 2b: Special Angle Pairs Postulate and Theorems

Source: Topic 2, Day 2 Notes

Special Angle Pairs Postulate/Theorems

Two PARALLEL LINES and a TRANSVERSAL

Same-Side Interior Angles Postulate

If a transversal intersects two PARALLEL lines, then same-side interior angles are SUPPLEMENTARY (*NOT add up to 180!!!)

Alternate Interior Angles Theorem

If a transversal intersects two PARALLEL lines, then alternate interior angles are congruent

Corresponding Angles Theorem

If a transversal intersects two PARALLEL lines, then corresponding angles are congruent

Alternate Exterior Angles Theorem

If a transversal intersects two PARALLEL lines, then alternate exterior angles are congruent

CONVERSE of Same-Side Interior Angles Postulate

If two lines and a transversal form same-side interior angles that are SUPPLEMENTARY, then the two lines are PARALLEL

CONVERSE of Alternate Interior Angles Theorem

If two lines and a transversal form alternate interior angles that are congruent, then the two lines are PARALLEL

CONVERSE of Corresponding Angles Theorem

If two lines and a transversal form corresponding angles that are congruent, then the two lines are PARALLEL

CONVERSE of Alternate Exterior Angles Theorem

If two lines and a transversal form alternate exterior angles that are congruent, then the two lines are PARALLEL

Difference Between a Theorem and the Converse of that Theorem

Theorem is used when given a geometric symbol (ex: ℓ || 𝓂) and you have to find the property (ex: ∠2 ≅ ∠6). Converse is used the opposite way.

Congruent SUPPLEMENTS Theorem

If two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent (*USED when proving a step in a proof that says SUPPLEMENTS instead of ‘add to 180’)

Congruent COMPLEMENTS Theorem

If two angles are complements of the same angle (or of congruent angles), then the two angles are congruent (*USED when proving a step in a proof that says COMPLEMENTS instead of ‘add to 90’)

Theorem 1-4

All right angles are congruent (*MUST write this out in ‘reason’ section because the theorem has no name)

Theorem 1-5

If two angles are congruent and supplementary, then each is a right angle (*MUST write this out in ‘reason’ section because the theorem has no name)