Parallel line
What is a parallel line?
A Parallel line is 2 or more lines where they never intersect
What is a transversal line?
a line that cuts across two or more lines in the same plane.
How are same-side interior angles related?
Supplementary
Identify which of the following pairs of angles are adjacent:
a) Two angles sharing only a vertex
b) Two angles sharing a vertex and a side, but not overlapping
c) Two angles sharing a side but with different vertices
d) Two overlapping angles
What is a corresponding angle?
Corresponding angles occur when a transversal line crosses two parallel lines.
Do Parallel lines eventually intersect?
No, they never intersect, no matter how far you try to extend them in any given direction.
In a figure where a transversal intersects two parallel lines, what is the relationship between corresponding angles?
Congruent
How are alternate interior angles related?
Congruent
In a figure, angle B measures 30 degrees and is adjacent to angle C. If B and C are supplementary, what is the measure of angle C?
150
Two parallel lines are intersected by a transversal. One of the corresponding angles measures 115°. What is the measure of its corresponding angle on the other parallel line?
115o
Why do parallel lines never intersect
the distance between them will never be zero.
How many degrees is a transversal line?
180 degrees
How can interior angles be used to determine if two lines are parallel?
If the alternate interior are congruent and/or the same-side interior angles are supplementary.
Two adjacent angles have measures expressed as (3x + 15)° and (2x + 30)°. If these angles are supplementary, find the value of x.
(3x+15)+(2x+30)=180
5x+45=180
5x=135
x=27
When are corresponding lines equal?
if a transversal intersects two parallel lines, the corresponding angles will be always equal.
Parallel lines intersect at any point
False
What is the purpose of a transversal line
Transversals play a role in establishing whether two or more other lines in the Euclidean plane are parallel.
Two parallel lines are intersected by a transversal. The measure of one same-side interior angle is given by the expression (3x + 15)°, while the measure of the other same-side interior angle is (2x + 30)°. What is the value of x?
5x=135
x=27
Angle A is adjacent to angle B, which is adjacent to angle C. If angle A measures 35°, angle C measures 70°, and all three are supplementary, determine the measure of angle B.
B=75o
Two parallel lines are cut by a transversal. The measure of one corresponding angle is given by the expression (3x + 15)°, while the measure of its corresponding angle on the other parallel line is (2x + 30)°. Find the value of x and the measures of both angles.
Since corresponding angles are congruent, we can set up the equation:
(3x + 15)° = (2x + 30)°
Solving this equation: x = 15
Substituting back: (3(15) + 15)° = 60° and (2(15) + 30)° = 60°
How many solutions does a parallel line have?
Zero Solutions
Two parallel lines are cut by a transversal. The measure of one of the alternate exterior angles is given by the expression (3x + 15)°, while the measure of one of the alternate interior angles is (2x + 30)°. Find the value of x and the measures of both angles.
Alternate exterior and alternate interior angles are congruent.
So, (3x + 15)° = (2x + 30)°
x = 15
Substitute back: (3(15) + 15)° = 60° and (2(15) + 30)° = 60°
In a figure where two parallel lines are intersected by a transversal, one alternate interior angle is given by the expression (7x - 20)° and the other by (4x + 10)°. Find the value of x.
7x-20=4x+10
3x=30
x=10
Two parallel lines are intersected by a transversal, two adjacent angles are formed at one of the intersection points. The measure of one angle is given by (2x + 10)°, and the measure of the adjacent angle is (3x - 20)°. Find the measures of both angles.
Set up the equation: (2x + 10)° + (3x - 20)° = 180°
Simplify: 5x - 10 = 180
Solve for x: 5x = 190, x = 38
Calculate the angles:
First angle: 2(38) + 10 = 86°
Second angle: 3(38) - 20 = 94°
In a figure, lines are intersected by a transversal. The measure of one angle formed is 70°. Its corresponding angle on the other line measures 80°.
A. Are the two intersected lines parallel? Explain why or why not.
B. If these lines are extended, will they eventually intersect?
No. Corresponding angles should be congruent.
Yes.