7/4/20153-2: angles and parallel lines1 12 34 78 65 l m t 12 34 78l m t 5 6
TRANSCRIPT
04/19/23 3-2: Angles and Parallel Lines 1
12
3 4
78
6 5
l
m
t
12
3 4
78 l
m
t
56
04/19/23 3-2: Angles and Parallel Lines 2
3-2: Angles and Parallel Lines
Expectation:
G1.1.1 : Solve multistep problems and construct proofs involving vertical angles, linear pairs of angles, supplementary angles, complementary angles, and right angles.
G1.1.2: Solve multi-step problems and construct proofs involving corresponding angles, alternate interior angles, alternate exterior angles, and same-side (consecutive) interior angles.
04/19/23 3-2: Angles and Parallel Lines 3
Parallel Lines and Angles
Using the diagram on your graphic organizer, make conjectures about consecutive interior, corresponding, alternate interior and alternate exterior angles.
04/19/23 3-2: Angles and Parallel Lines 4
Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then corresponding angles are ____________.
04/19/23 3-2: Angles and Parallel Lines 5
Alternate Interior Anglesl
m
t
1 23 45 67 8
Given: l || mProve: 3 ∠ ≅ 6∠
04/19/23 3-2: Angles and Parallel Lines 6
04/19/23 3-2: Angles and Parallel Lines 7
04/19/23 3-2: Angles and Parallel Lines 8
Alternate Interior Angle Theorem
If two parallel lines are cut by a transversal, then alternate interior angles are _____________.
04/19/23 3-2: Angles and Parallel Lines 9
l
m
t
1 23 45 67 8
If l // m, m 3 = 4x + 12 and m 6 = 9x – 18, determine ∠ ∠the value of x and the measure of all 8 angles.
04/19/23 3-2: Angles and Parallel Lines 10
Alternate Exterior Angle Theorem
If two parallel lines are cut by a transversal, then alternate exterior angles are _____________.
04/19/23 3-2: Angles and Parallel Lines 11
Consecutive Interior Anglesl
m
t
1 23 45 67 8
Given: l || mProve: 3 is ______________ 5 ∠ ∠
04/19/23 3-2: Angles and Parallel Lines 12
04/19/23 3-2: Angles and Parallel Lines 13
04/19/23 3-2: Angles and Parallel Lines 14
Consecutive Interior Angle Theorem
If two parallel lines are cut by a transversal, then consecutive interior angles are _________________.
04/19/23 3-2: Angles and Parallel Lines 15
Consecutive Exterior Angle Theorem
If two parallel lines are cut by a transversal, then consecutive exterior angles are _________________.
04/19/23 3-2: Angles and Parallel Lines 16
l
m
t
1 23 45 67 8
If l // m, m 1 = 5x - 1 and m 7 = 6x - 39, determine ∠ ∠the value of x and the measure of all 8 angles.
04/19/23 3-2: Angles and Parallel Lines 17
Perpendicular Transversals
l
m
tWhat is true about t and l? Why?
04/19/23 3-2: Angles and Parallel Lines 18
Perpendicular Transversal Theorem
In a plane, if a transversal is perpendicular to one of 2 parallel lines, then it is _______________ to the other line as well.
04/19/23 3-2: Angles and Parallel Lines 19
In the figure, BG // CE, BE //CD, BG bisects EBA, m 8 = 42 and m 3 = 18. ∠ ∠ ∠
Determine the measure of each angle.
04/19/23 3-2: Angles and Parallel Lines 20
Determine the values of y and z.
In the figure showing ΔPQR below, line l is parallel to line m. Which one of the following angles must be congruent to ∠y?
A) 1∠B) 2∠C) 3∠D) 4∠E) 5∠
04/19/23 3.3: Parallel Line
s and Transv
ersals
l
m
Q
1 2 y
345
04/19/23 3-2: Angles and Parallel Lines 22
pages 135-137,
#17- 25 (all), 39, 43 and 50
Assignment