Geometry Transversal and Slope unit

​Transversals

​

• A transversal is a line that intersects at least two other lines

• ​The two other lines, l₁ and l₂ in the diagram, could be parallel, but do not have to be

​

​If 2 parallel Lines are cut by a transversal, then...

• ​alternate interior angles are congruent

• ​alternate exterior angles are congruent

• ​corresponding angles are congruent

• ​same-side (consecutive) interior angles are supplementary

Multiple Choice

Angle 1 = 27^o
Find the measure of angle 4

• 27^o
• 153^o
• 63^o
• 90^o

Multiple Choice

What type of angle pair is ∠1 and ∠3?

• alternate interior angles

• linear pair

• corresponding angles

• vertical angles

Multiple Choice

In the diagram, which of the following statements are false?

• ∠1 and ∠4 are vertical angles
• ∠4 and ∠5 are alternate interior angles
• ∠1 and ∠8 are alternate interior angles
• ∠2 and ∠6 are corresponding angles

Multiple Choice

Name the alternate interior angle to angle 3.

• 4
• 5
• 6
• 8

Multiple Choice

What angle pair is pictured?

• Alternate Interior Angles

• Supplementary Angles

• Vertical Angles

• Corresponding Angles

Multiple Choice

A line that passes through 2 or more lines is called a ______________.

• transitive
• passer through line
• transversal
• bisector

Multiple Choice

What is the value of y?

• 29
• 119
• 58

Multiple Choice

Solve for  y.

• y = 20
• y = 120
• y = 60
• y = 10

Multiple Choice

Name the angle relationship.

• Alternate Interior
• Alternate Exterior
• Corresponding
• Vertical Angles

Multiple Choice

If angle 1 is 135 degrees, how many degrees is angle 3?

• 45 degrees

• 65 degrees

• 135 degrees

• 225 degrees

Multiple Choice

What angle is the same side interior angle to angle 4?

• angle 3

• angle 5

• angle 6

• angle 8

Multiple Choice

REVIEW: What is the slope of the line:  $$y=\frac{2}{3}x+4$$  

• $$\frac{2}{3}$$  

• $$-\frac{2}{3}$$  

• $$\frac{3}{2}$$  

• $$4$$  

• $$-4$$  

Multiple Choice

How many points do you need to find the slope of a line?

• 1

• 2

• 3

• 4

​

Step by Step:

• 1. Label the Points 1 and 2 (Slope is ALWAYS the same, no matter which point you pick to be the “first” or “second”.)

• 2. Label the X and Y for each point

• 3. Write the values in the slope formula

• 4. Simplify

​

Practice

Find the slope of the line that goes through the points (5, 17) and (0,-3).

Step 1: Label the Points

• First Point ------> (X₁, Y₁) = (5, 17)

• Second Point ------> (X₂, Y₂) = (0, -3)

​

Step 2: Extract Values

• X₁ = 5 and Y₁ = 17

• X₂ = 0 and Y₂ = -3

​****Minusing a negative give you a positive!

​​Step 3: Plug the values into the slope formula.​

-Remember that Y values go on top and X values go on bottom. ​

-Make note of the MINUS in between each point for the top and bottom​

-Don't mix the first (red) and second (blue) points. 

​ PAY ATTENTION TO YOUR SIGNS!!!!

Step 4: Simplify

​

-Solve for m using the Order of Operations (PEMDAS)​

-Make sure that you subtract the numbers correctly. Use a CALCULATOR!

**Remember- subtracting a negative number is the same as adding

​

Multiple Choice

Find the slope of the line that goes through the points

(−11,−5) and (1,−12)

• $$-\frac{5}{8}$$  

• $$\frac{16}{11}$$  

• $$\frac{1}{6}$$  

• $$-\frac{7}{12}$$  

Multiple Choice

Find the slope of the line that goes through the points

(−1,−2) and (−3,−4).

• 1

• 2

• 3

• 4

SLOPE of Parallel Lines

In the coordinate plane,

Parallel Lines have the SAME SLOPE

In the coordinate plane,

Parallel Lines have the SAME SLOPE

Multiple Select

Which two lines are parallel?

• $$y=\frac{3}{7}x-25$$

• $$y=\frac{3}{7}x+2$$

• $$y=\frac{7}{3}x-25$$

• $$y=3x+13$$

• $$y=7x+9$$

Multiple Choice

What slope is parallel to a slope of 2?

• 1

• $$-\frac{1}{2}$$

• $$\frac{1}{2}$$

• 2

Multiple Select

Which two lines are parallel?

• $$y=-\frac{1}{4}x-25$$

• $$y=\frac{1}{4}x+2$$

• $$y=-4x-25$$

• $$y=4x+13$$

• $$y=\frac{1}{4}x+9$$

Multiple Choice

Which of the following equations is parallel to  $$y=\frac{1}{2}x+5$$  ?

• $$y=-\frac{1}{2}x-3$$  

• $$y=-2x+4$$  

• $$y=\frac{1}{2}x-3$$  

• $$y=\frac{1}{2}x+5$$  

In the coordinate plane, Perpendicular Lines

have slopes that are OPPOSITE RECIPROCALS

SLOPE of Perpendicular Lines

In the coordinate plane, Perpendicular Lines

have slopes that are OPPOSITE RECIPROCALS

Multiple Choice

What is the reciprocal of:  $$\frac{8}{5}$$  

• $$\frac{8}{5}$$  

• $$-\frac{8}{5}$$  

• $$-\frac{5}{8}$$  

• $$\frac{5}{8}$$  

Multiple Choice

Which equation is perpendicular to  $$y=\frac{2}{3}x-4$$ ?

• $$y=-\frac{3}{2}x+4$$  

• $$y=-\frac{2}{3}x+4$$  

• $$y=\frac{2}{3}x-4$$  

• $$y=\frac{3}{2}x-4$$  

Multiple Select

Which two lines are perpendicular?

• $$y=\frac{3}{7}x-25$$

• $$y=-\frac{3}{7}x+2$$

• $$y=-\frac{7}{3}x-25$$

• $$y=3x+13$$

• $$y=7x+9$$

What about equations in different forms?

Multiple Choice

Convert the standard form equation into slope-intercept form.

6x - 7y = -35

• $$y=\frac{7}{6}x-5$$

• $$y=\frac{6}{7}x+5$$

• $$y=\frac{5}{7}x-6$$

• $$y=-\frac{6}{7}x-5$$

Multiple Choice

Are the given lines parallel, perpendicular, or neither? $$y=\frac{1}{2}x+2$$  and $$y=\frac{1}{2}x-4$$  

• Parallel

• Perpendicular

• Neither

Multiple Choice

Are the given lines parallel, perpendicular, or neither? $$y=2x+3$$  and  $$y=-\frac{1}{2}x+3$$  

• Parallel

• Perpendicular

• Neither