angle pair proofs with rules.notebook - mclean county unit ... pair proofs with rules.pdfangle pair...
TRANSCRIPT
Angle pair proofs with rules.notebook
1
October 04, 2016
Proof of WHY vertical angles are congruent
1. Name both pairs of vertical angles in the picture.
2. What do we know about the relationship of vertical angles? (≅ or +180?)
3. Name all four linear pairs in the picture. 4. What do we know about the relationship of linear pairs?
Proof of the vertical angles theorem:Given: ∠1 and ∠2 are vertical anglesClaim: ∠1 ≅ ∠2
_______________ are a linear pair, so they are _____________________. Therefore, ____________________.
______________ are a linear pair, so they are ______________________. Therefore, ____________________.
Since both pairs sum to ___________________, we can ____________________________________________.
Algebra:
Therefore, ∠1 ≅ ∠2.
Angle pair proofs with rules.notebook
2
October 04, 2016
Angle pair proofs with rules.notebook
3
October 04, 2016
Angle pair proofs with rules.notebook
4
October 04, 2016
Angle pair proofs with rules.notebook
5
October 04, 2016
Converse theorems: we don’t know these lines are parallel (despite the visual), so we don’t know the previous theorems exist.
Rule 8. If you can show you have a pair of corresponding angles that are congruent, then you can show two lines are parallel.
Example: If ∠1 and ∠9 are congruent, THEN l // m (but a is NOT guaranteed parallel to b).
Angle pair proofs with rules.notebook
6
October 04, 2016
Converse theorems: we don’t know these lines are parallel (despite the visual), so we don’t know the previous theorems exist.
Rule 9. If you can show you have a pair of alternate interior angles that are congruent, then you can show two lines are parallel.
Example: If ∠4 ≅ ∠5, THEN a // b (but l is NOT guaranteed parallel to m).
Angle pair proofs with rules.notebook
7
October 04, 2016
Converse theorems: we don’t know these lines are parallel (despite the visual), so we don’t know the previous theorems exist.
Rule 10. If you can show you have a pair of alternate exterior angles that are congruent,then you can show two lines are parallel.
Example: If ∠1 ≅ ∠12, THEN l // m (but a is NOT guaranteed parallel to b).
Angle pair proofs with rules.notebook
8
October 04, 2016
Converse theorems: we don’t know these lines are parallel (despite the visual), so we don’t know the previous theorems exist.
Rule 11. If you can show you have a pair of same side interior angles that are supplementary, then you can show two lines are parallel.
Example: if ∠4 and ∠7 are supplementary, THEN a // b (but l is NOT guaranteed parallel to m)
Angle pair proofs with rules.notebook
9
October 04, 2016
Converse theorems: we don’t know these lines are parallel (despite the visual), so we don’t know the previous theorems exist.
Rule 12. If you can show you have a pair of same side exterior angles that are supplementary, then you can show two lines are parallel.
Example: If ∠1 and ∠11 are supplementary, THEN l // m (but a is not guaranteed parallel to b).
Angle pair proofs with rules.notebook
10
October 04, 2016
Angle pair proofs with rules.notebook
11
October 04, 2016
Determine which lines, if any, are parallel given the following information. Write the rule that supports your claim.
Example 1: Example 2: Example 3:
Given: ∠4 ≅ ∠12 Given: ∠11 ≅ ∠7 Given: ∠2 and ∠5 are supplementary
Which lines are parallel? Which lines are parallel? Which lines are parallel?
Angle pair proofs with rules.notebook
12
October 04, 2016
Angle pair proofs with rules.notebook
13
October 04, 2016