Unit 2 - Angles of Geometry - Proofs and Justifications

Question 1

Definition of Supplement Theorem

Answer 1

Linear pairs sum to 180

Question 2

Angle Addition Postulate

Answer 2

When two angles are added together, they sum to the whole angle (for proofs, you can just say angle addition postulate).

Question 3

Vertical Angle Theorem

Answer 3

Vertical angles are congruent

Question 4

Corresponding Angle Postulate

Answer 4

If 2 parallel lines are cut by a transversal, corresponding angles are congruent.

Question 5

Alternate Interior Angle Postulate

Answer 5

If 2 parallel lines are cut by a transversal, alternate interior angles are congruent
(To identify, the lines create a z)

Question 6

Consecutive Interior Angles Postulate

Answer 6

If 2 parallel lines are cut by the transversal, consecutive interior angles are supplementary.

Question 7

Alternate Exterior Angles Theorem

Answer 7

If 2 parallel lines are cut by the transversal, alternate exterior angles are congruent.

Question 8

Converse of the Corresponding Angles Postulate

Answer 8

If 2 lines are cut by a transversal such that corresponding angles are congruent, then the lines are parallel.

Question 9

Converse of the Alternate Interior Angles Theorem

Answer 9

If 2 lines are cut by a transversal such that alternate interior angles are congruent, then the lines are parallel.

Question 10

Converse of the Consecutive Interior Angles Theorem

Answer 10

If 2 lines are cut by a transversal such that consecutive interior angles are supplementary then the lines are parallel.

Question 11

Converse of the Alternate Exterior Angles Theorem

Answer 11

If 2 lines are cut by a transversal such that alternate exterior angles are congruent, then the lines are parallel.

Question 12

Converse of the Perpendicular Transversal Theorem

Answer 12

If 2 lines are perpendicular to the same lines, then they are parallel to each other.
(forms two right angles that are consecutive interior)

Question 13

What are the 5 ways that proves that a pair of lines are parallel?

Answer 13

1. Converse of Corresponding Angle Postulate
2. Converse of Alternate Interior Angle Theorem
3. Converse of Alternate Exterior Angle Theorem
4. Converse of Consecutive Interior Angle Theorem
5. Converse of the Perpendicular Transversal Theorem

Question 14

What are the two reasons why something is not parallel?

Answer 14

1. Congruent angles form, but not because of the 5 reasons
2. Found on COMPLETELY different transversals

Question 15

Why do we use auxiliary lines?

Answer 15

Often in geometry, it is helpful to modify the figure in order to find certain info. It is never acceptable to change of the original parts of the figure, but it is allowed to draw in dotted lines that help demonstrate something.

Question 16

What do you say in justification for the isosceles sides and angles?

Answer 16

In a triangle, angles opposite congruent sides are congruent.

Question 17

What do you say in justification for the Exterior Angles Theorem?

Answer 17

Exterior angle is equal to the sum of the remote interior angles.

Question 18

What do you say in justification for the adjacent angles?

Answer 18

Adjacent angles on a line sum to 180 degrees

Question 19

What do you say in proofs for angle bisectors?

Answer 19

An angle bisector divides an angle into two congruent angles.

Question 20

What do you say in proofs when you replace a variable?

Answer 20

Substitution

Question 21

How do you construct parallel lines parallel to Line AB through Point C using the converse of the corresponding angle postulate? (12)
(Line AB and Point C)

Answer 21

1. Construct a transversal passing through C & AB
2. Intersection at AB as D
3. Construct arc at point D
4. Intersection of arc & CD is E
5. Intersection of arc & BD is F
6. Copy arc at point C (SAME SIDE AS ARC AT D)
7. Intersection of arc & line CD (ABOVE POINT C) is G
8. Measure angle of E & F
9. Copy angle from point G
10. Intersection of angle & arc is now H
11. Congruent Corresponding Angles are Formed!
12. Line HC is II to Line AB!

Question 22

How do you construct parallel lines parallel to Line AB through Point C using the converse of the alternate angle postulate? (12)
(Line AB and Point C)

Answer 22

1. Construct a transversal passing through C & AB
2. Intersection at AB as D
3. Construct arc at point D
4. Intersection of arc & CD is E
5. Intersection of arc & BD is F
6. Copy arc at point C (OPP. SIDE OF ARC AT D)
7. Intersection of arc & line CD (BELOW POINT C) is G
8. 8. Measure angle of E & F
9. Copy angle from point G
10. Intersection of angle & arc is now H
11. Congruent Alt. Int. Angles are Formed!
12. Line HC is II to Line AB!