CHAPTER 7 REVIEW

By Sarah & Gabby

7-1 PARALLEL LINES AND RELATED ANGLES

A transversal is a line that intersects two coplanar lines at two distinct points.

The blue line is a transversal.

7-1 PARALLEL LINES AND RELATED ANGLES

Corresponding angles are always congruent. Think of them as “sliders”. They slide down a transversal and land on its corresponding angle.

<A & <B are corresponding angles.

7-1 PARALLEL LINES AND RELATED ANGLES

Alternate interior angles are also always congruent. They are found inside the parallel lines and on opposite sides of the transversal.

<A & <D are alternate interior angles.

7-1 PARALLEL LINES AND RELATED ANGLES

Same side interior angles are supplementary. They are located on the interior and on the same side of the transversal.

<3 and <5 are same side interior angles. <4 and <6 are also same side interior

angles.

7-2 PROVING LINES PARALLEL

If two lines are cut by a transversal so that a pair of corresponding angles are congruent, then the lines are parallel.

If <Q=<R, then AB ll CD.

7-2 PROVING TWO LINES PARALLEL

If two lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the lines are parallel.

If <3=<6, then p ll q.

7-2 PROVING TWO LINES PARALLEL

If two lines are cut by a transversal so that a pair of same side interior angles are supplementary, then the lines are parallel.

If <4 and <6 are supplementary, then p ll q.

GRAPHING LINES

The standard equation of a line in y-intercept form is:

y=mx+b

By using this equation, you can tell if two lines are parallel, perpendicular, or neither, without graphing them.

For example, parallel lines have the same slope: y=5x+3 and y=5x+7 are parallel lines since they both have a slope of 5.

GRAPHING LINES

You can also determine perpendicular lines. For example: y=3x-4 and y=-1/3x-7 are perpendicular because their slopes are negative reciprocals of each other.

If the slopes are not equal or negative reciprocals of each other, you cannot determine them to be parallel or perpendicular. Example: y=4x+7 and y=-6x-9 are neither parallel nor perpendicular.

GRAPHING LINES

In order to graph the equation y=-2x+4, first you must graph the y intercept, which is 4.

Once you mark your point on the y-axis, you determine the slope. In this equation, the slope is -2 or -2/1.

When you graph a line, the slope is rise over run. Therefore, you would go 2 down since the slope is negative, followed by 1 to the right. After you’ve placed your points on the graph, you end up with a line that looks like this:

GRAPHING LINES

DETERMINING SLOPE

To find the slope of a line we use the formula: m=y2-y1

x2-x1

Example: A(1,3) B(2,5) m=5-3 2-1

The slope is 2/1 or 2.

BINGO GAME

BINGO

Find the value of x.

ANSWER: x=65

BINGO

Are the lines parallel, perpendicular, or neither?

y=3x-4y=-1/2x+3.

ANSWER: neither

BINGO

Find the value of x.

ANSWER: x=21

BINGO

Are the lines parallel, perpendicular, or neither?

X=4Y=-2

ANSWER: perpendicular

BINGO

Find the measure of <1.

ANSWER: <1=40

BINGO

Find the slope of:

A(2,0) B(2,4)

ANSWER: undefined

BINGO

Find the measure of angles 2 & 3.

ANSWER: <2=40 <3=140

BINGO

If <2=85, find the m<6.

ANSWER: m<6=85

BINGO

Determine the slope and tell if the lines are parallel, perpendicular or neither.

A(0,3) B(-2,3) and C(5,-1) D(5,3)

ANSWER: 0/-2 ; 4/0 ; perpendicular

BINGO

Determine the slope of points A & B .

A(-3,5) B(2,3)

ANSWER: 2/-5

BINGO

Find the measure of <H.

ANSWER: <H= 110

BINGO

What type of angles are <1 and <5?

ANSWER: corresponding angles

BINGO

Find the slope of:

A(-4,1) B(1,3)

ANSWER: -2/-5 (2/5)

BINGO

What type of angles are <3 and <6?

ANSWER: alternate interior angles

BINGO

What type of angles are <3 and <5?

ANSWER: same side interior angles

BINGO

Give the angle to make the following true, <7=_______.

ANSWER: < 3