4.3 – Proving Lines are Parallel

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Presentation transcript:

4.3 – Proving Lines are Parallel Fill in your notes

Recall: Conditional statement: If a, then b. CONVERSE statement: If b, then a. For the converse, we just switch the hypothesis and conclusion

Ex: If ∠3 ≅ ∠7, then j // k Corresponding Angles Converse - If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. Ex: If ∠3 ≅ ∠7, then j // k

Ex: If ∠3 ≅ ∠6, then j // k Alternate Interior Angles Converse - If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel. Ex: If ∠3 ≅ ∠6, then j // k

Ex: If ∠1 ≅ ∠8, then j // k Alternate Exterior Angles Converse - If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel. Ex: If ∠1 ≅ ∠8, then j // k

Ex: If m∠3 + m∠5=180°, then j // k Consecutive (Same-Side) Interior Angles Converse - If two lines are cut by a transversal so that consecutive (same-side) interior angles are supplementary, then the lines are parallel. Ex: If m∠3 + m∠5=180°, then j // k

Vertical Angles are ≅ Transitive POC Corresponding Angles CONVERSE

Which lines are parallel? Why? **Figures not drawn to scale 120+ 60 = 180 So ∠CHA and ∠DAH are supplementary CH // AD Which lines are parallel? Why? **Figures not drawn to scale

Which lines are parallel? Why? **Figures not drawn to scale 80° Linear pair 80 = 80 The two 80° angles are congruent AND corresponding, so….. l // m Which lines are parallel? Why? **Figures not drawn to scale

Which lines are parallel? Why? **Figures not drawn to scale 50 = 50 ∠BAC and ∠DCA are congruent and alternate interior angles So… BA // CD 30° Because a triangle adds to 180. And the 30 and 20 are not equal so BC is not parallel to AD Which lines are parallel? Why? **Figures not drawn to scale

Which lines are parallel? Why? (Try these on your own) J // k l // m none l // m J // k Which lines are parallel? Why? (Try these on your own)

The two angles are corresponding angles, so for j//k they have to be congruent (equal) 3x + 5 = 65 3x = 60 x = 20

The two angles are consecutive (same-side) interior angles, so for j//k they have to be supplementary X + 4x = 180 5x = 180 x = 36

m // n n // k Corresponding angles Theorem Corresponding angles Theorem Transitive Corresponding angles CONVERSE m // k

EXACTLY ONE!