Geometry Warm UpsWeek of February 11-15

DFA Review

•This our last week of preparing for the DFA.

•Please make sure you understand these concepts.

•There will be a quiz on Friday.

Monday #1

Solve the following equation for x:

5x - 3 = 3x + 9-3x +32x = 12x = 6

Monday #2

• bisects Find the value of x.

A bisector is something that cuts another thing in half, creating two congruent parts. So here, 30 = 5x. It’s easy to see that x = 6.

Monday #3

•In the figure bisects If m and m, what is the measure of ABD?

With this bisector, the angles are congruent. So 6x + 8 = 8x – 2.

Solving for x +2 -6x 10 = 2x 5 = x

Tuesday #1

•Which equation shown below is a line that passes through the point (1, 7)?

A. y = 5x – 4B. y = 5x + 2C. y = 5x – 3

Use your calculator!

Substitute 1 for x into each choice, only one will give 7 as the answer, which is y.

Tuesday #2

•Which equation shown below is a line that passes through the point (2, -3) and is parallel to the line whose equation is 10x – 5y = 4?

A. y = 2x – 7 B. y = 2x – 3C. y = 2x + 2

Use your calculator!

Is this part even

necessary?

No, each choice has a slope of 2.

Substitute 2 for x into each, only one will give -3 as the answer.

Tuesday #3

•Which equation represents a line that is parallel to the line whose equation is 18x – 3y = 6 and passes through the point (7, 12)?

A. y = 6x + 7 B. y = 6x – 6 C. y = 6x – 12 D. y = 6x – 30

Since each choice has the exact same slope, there is no need to figure out the slope of the given equation. Just substitute 7 for x into each choice, only D gives the correct answer of 12.

Wednesday/Thursday #1

•What is the midpoint of ?

One way to do this is to put the coordinates into the Midpoint Formula, listed on the math formula chart.

An easier alternative is to use the slope. From point A to B, you have to go up 4 and to the left 6. Just go halfway and you will locate the midpoint.

Wednesday/Thursday #2

•M is the midpoint of . What are the coordinates of B?

To find the other endpoint, figure out to get from A to M. Repeat that from M to find B…another application of slope.

Wednesday/Thursday #3

•M is the midpoint of . If the coordinates of A are (-2, 4) and the coordinates of M are (-3, 1), what are the coordinates of B?

Very similar to the last question but in order to save time on drawing a grid and plotting points…Draw a small segment and label one end with A and the middle with M. Figure out how the numbers changed and repeat that process…just like a transformation.

A (-2, 4) M(-3, 1) B(-4, -2)

Wednesday/Thursday #4

•Line l and line m are perpendicular. If the slope of line l is ¼, what is the slope of line m?

•Line p and line q are parallel. If the slope of line p is 1/3, what is the slope of line q?

Perpendicular lines have slope that are opposite reciprocals; their product is -1 so the answer here is -4

Parallel lines have the same slope so the answer here would be 1/3

Wednesday/Thursday #5

•Rectangle ABCD is shown below. If the slope of is ¼, what is the slope of ?

Rectangles have 4 right angles and perpendicular sides. This means the slope of CD would be ¼ and for extra credit, the slopes of AD and BC would be -4.

Extra Note: The product of the slope of perpendicular lines has to be -1.

Wednesday/Thursday #6

•In rectangle ABCD, the slope of is . What is the slope of ?

A B

CD

Very Important: The letters of a figure must go in one order…clockwise or counterclockwise and it does not matter where you start.

This way you get the right slope.The answer is 2/3.

Friday – Quiz #1

•In the figure bisects If m and m, what is the measure of ABD?

Friday – Quiz #2

•Which equation represents a line that is parallel to the line whose equation is 12x – 4y = 6 and passes through the point (-3, -1)?

A. y = 3x + 8 B. y = 3x – 6 C. y = 3x – 1 D. y = 3x – 3

Friday – Quiz #3

•M is the midpoint of . If the coordinates of A are (-4, -3) and the coordinates of M are (-3, 1), what are the coordinates of B?

Friday – Quiz #4

•In rectangle WXYZ, the slope of is 1/5. What is the slope of ?