Parallel lines
Parallel Lines- 2 or more lines that will never intersect and are coplanar.
-What problems would there be in your picture if the lines were not parallel? If the tracks are not parallel, the wheels will not stay on the tracks because train wheels are spaced at a fixed width and that width cannot expand or contract to accommodate non-parallel tracks. If the tracks were non-parallel, the wheel would come off the track.
-Are the lines cut by a transversal? No
-Explain how the lines in the picture are parallel. They are parallel because they will never intersect.
-Can you identify any angles in your picture? If so, what kind? Yes, I can identify right angles.
o How do you prove lines parallel? You prove that lines are parallel by showing that lines perpendicular from the same line are parallel to each other.
-What problems would there be in your picture if the lines were not parallel? If the tracks are not parallel, the wheels will not stay on the tracks because train wheels are spaced at a fixed width and that width cannot expand or contract to accommodate non-parallel tracks. If the tracks were non-parallel, the wheel would come off the track.
-Are the lines cut by a transversal? No
-Explain how the lines in the picture are parallel. They are parallel because they will never intersect.
-Can you identify any angles in your picture? If so, what kind? Yes, I can identify right angles.
o How do you prove lines parallel? You prove that lines are parallel by showing that lines perpendicular from the same line are parallel to each other.
Slope
Slope- the slope of a non-vertical lines is the ratio of the rise to the run between any two points on the line.
-What problems would there be in your picture if the object did not have a slope? People who are trying to go to a lower level would not would not be able to get there.
-What type of slope does your object have? My object has a negative slope.
-Explain how to find the slope of a line given the coordinates of two points on the line. If a line in the coordinate plane passes through points (x sub1, y sub1) and (x sub2, y sub2)then the slope m is m=rise = y2-y1.
run x2-x1
-What problems would there be in your picture if the object did not have a slope? People who are trying to go to a lower level would not would not be able to get there.
-What type of slope does your object have? My object has a negative slope.
-Explain how to find the slope of a line given the coordinates of two points on the line. If a line in the coordinate plane passes through points (x sub1, y sub1) and (x sub2, y sub2)then the slope m is m=rise = y2-y1.
run x2-x1
Vertical Angles
Vertical Angles- Two angles whose sides form two pairs of opposite rays.
- Why do you think the person that created the vertical angles in your picture did so? The scissors have two pairs of vertical angles. Angles 1 and 2 are opposite rays, while angles 3 and 4 are also opposite rays. No matter how far apart you put the blades of the scissor there will still be two vertical angles, because the degrees of the angle will change equally always having two opposite rays. Scissors have vertical angles to allow paper to fit into the blades to be cut.
-What is the relationship between vertical angles, between two angles that are supplementary to the same angle, and between two angles that are complementary to the same angle? If two angles are supplementary to the same angle , then they are congruent. If two angles are complementary to the same angle, then they are congruent. Vertical angles are congruent.
- Why do you think the person that created the vertical angles in your picture did so? The scissors have two pairs of vertical angles. Angles 1 and 2 are opposite rays, while angles 3 and 4 are also opposite rays. No matter how far apart you put the blades of the scissor there will still be two vertical angles, because the degrees of the angle will change equally always having two opposite rays. Scissors have vertical angles to allow paper to fit into the blades to be cut.
-What is the relationship between vertical angles, between two angles that are supplementary to the same angle, and between two angles that are complementary to the same angle? If two angles are supplementary to the same angle , then they are congruent. If two angles are complementary to the same angle, then they are congruent. Vertical angles are congruent.
Perpendicular lines
Perpendicular Lines- two lines that intersect to form a right angle.
-Would there be a consequence if the lines were not perpendicular? If the building was not perpendicular to the ground then the building would not be stable. Also the building would be "sitting on air".
-How do you determine the slope of perpendicular lines? In a coordinate plane, two non-vertical lines are perpendicular if and only if the product of their slope is -1. The formula is m sub 1 time m sub 2 equals negative one. Example: Find the slope m sub 1 of line h through (3,0) and (7,6). Find the slope m sub 2 of a line perpendicular to h. Use the fact that the product of the slope of two perpendicular lines is negative one.
-Would there be a consequence if the lines were not perpendicular? If the building was not perpendicular to the ground then the building would not be stable. Also the building would be "sitting on air".
-How do you determine the slope of perpendicular lines? In a coordinate plane, two non-vertical lines are perpendicular if and only if the product of their slope is -1. The formula is m sub 1 time m sub 2 equals negative one. Example: Find the slope m sub 1 of line h through (3,0) and (7,6). Find the slope m sub 2 of a line perpendicular to h. Use the fact that the product of the slope of two perpendicular lines is negative one.
Intersecting Lines
Intersecting Lines- Two or more lines that meet at a point.
-Why is it important that these lines intersect? If these lines did not intersect then all roads would be one way. But travel is not all in the same direction. Our chosen line of traffic often must cross the paths of other vehicles. If there were no intersecting lines on roads then traffic could not travel in two directions.
-Why is it important that these lines intersect? If these lines did not intersect then all roads would be one way. But travel is not all in the same direction. Our chosen line of traffic often must cross the paths of other vehicles. If there were no intersecting lines on roads then traffic could not travel in two directions.