Unit 3 Proving Lines are Parallel Prove Theorems

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Unit 3 Proving Lines are Parallel Prove Theorems about Perpendicular lines

Unit 3 Proving Lines are Parallel Prove Theorems about Perpendicular lines

Name Corresponding Angles Converse Description If ____ 1 _____, 5 then m n

Name Corresponding Angles Converse Description If ____ 1 _____, 5 then m n

Name Alternate Interior Angles Converse Description If ____ 3 _____, 6 then m n

Name Alternate Interior Angles Converse Description If ____ 3 _____, 6 then m n

Name Alternate Exterior Angles Converse Description If ____ 1 _____, 7 then m n

Name Alternate Exterior Angles Converse Description If ____ 1 _____, 7 then m n

Name Description Consecutive Interior 180° If ____ + _____ = _____, then 3 5

Name Description Consecutive Interior 180° If ____ + _____ = _____, then 3 5 Angles Converse m n

1. Is there enough information to prove the lines are parallel? If yes, state

1. Is there enough information to prove the lines are parallel? If yes, state theorem you used. Yes, Corresponding Angles Converse

1. Is there enough information to prove the lines are parallel? If yes, state

1. Is there enough information to prove the lines are parallel? If yes, state theorem you used. No

1. Is there enough information to prove the lines are parallel? If yes, state

1. Is there enough information to prove the lines are parallel? If yes, state theorem you used. Yes, Alternate Interior Angles Converse

2. What value of x makes theorem you used. ? State which Alternate Exterior

2. What value of x makes theorem you used. ? State which Alternate Exterior Angles Converse 5 x + 20 = 90 5 x = 70 x = 14°

2. What value of x makes theorem you used. ? State which Corresponding Angles

2. What value of x makes theorem you used. ? State which Corresponding Angles Converse 4 x – 28 = 100 4 x = 128 x = 32°

2. What value of x makes ? State which theorem you used. Consecutive Interior

2. What value of x makes ? State which theorem you used. Consecutive Interior Angles Converse 2 x + 36 + 4 x = 180 6 x + 36 = 180 6 x = 144 x = 24

intersect If two lines __________ to form a linear pair of ________ angles, then

intersect If two lines __________ to form a linear pair of ________ angles, then the congruent lines are __________. perpendicular

If two lines are __________, then perpendicular they intersect to form four _______ right

If two lines are __________, then perpendicular they intersect to form four _______ right angles.

If two sides of two adjacent acute angles are perpendicular ___________, then the angles

If two sides of two adjacent acute angles are perpendicular ___________, then the angles are complementary ____________. A B C

perpendicular If a transversal is ____________ to one of two parallel lines, then it

perpendicular If a transversal is ____________ to one of two parallel lines, then it is perpendicular ___________ to the other.

In a plane, if two lines are perpendicular __________ to the same line, then

In a plane, if two lines are perpendicular __________ to the same line, then parallel they are _________ to each other.

1. 2 x + 18 + 36 = 90 2 x + 54 =

1. 2 x + 18 + 36 = 90 2 x + 54 = 90 2 x = 36 x = 18°

1. 3 x – 11 + 38 = 90 38° 3 x + 27

1. 3 x – 11 + 38 = 90 38° 3 x + 27 = 90 3 x = 63 x = 21°

HW Problem LT 3. 1, 3. 2, 3. 3 165 -168 3, 5, 6,

HW Problem LT 3. 1, 3. 2, 3. 3 165 -168 3, 5, 6, 8, 10 -15, 19 194 -197 1, 5 -7, 17, 21, 31 (copy table) #31

m 1 + m 2 = 180 Def. of linear pair Def. of angles

m 1 + m 2 = 180 Def. of linear pair Def. of angles 1 is a right angle Division Prop. Def. of perp. lines

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