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Geometry Warm Ups

Geometry Warm Ups. Week 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 +3 2x = 12

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Geometry Warm Ups

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  1. Geometry Warm Ups Week of February 11-15

  2. 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.

  3. Monday #1 Solve the following equation for x: 5x - 3 = 3x + 9 -3x +3 2x = 12 x = 6

  4. 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.

  5. 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

  6. Use your calculator! Tuesday #1 • Which equation shown below is a line that passes through the point (1, 7)? • y = 5x – 4 • y = 5x + 2 • y = 5x – 3 Substitute 1 for x into each choice, only one will give 7 as the answer, which is y.

  7. Use your calculator! 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? • y = 2x – 7 • y = 2x– 3 • y = 2x + 2 Is this part even necessary? Substitute 2 for x into each, only one will give -3 as the answer. No, each choice has a slope of 2.

  8. 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)? • y = 6x + 7 • y = 6x – 6 • y = 6x – 12 • 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.

  9. 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.

  10. 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.

  11. 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)

  12. 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

  13. 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.

  14. Wednesday/Thursday #6 • In rectangle ABCD, the slope of is . What is the slope of ? 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. A B D C

  15. Friday – Quiz #1 • In the figure bisects If m and m, what is the measure of ABD?

  16. 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)? • y = 3x + 8 • y = 3x – 6 • y = 3x – 1 • y = 3x – 3

  17. 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?

  18. Friday – Quiz #4 • In rectangle WXYZ, the slope of is 1/5. What is the slope of ?

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