Draw a line l and a point P not on l. Construct a perpendicular to l through P. Describe the construction steps and prove the steps are valid (i.e., that the line you construct is perpendicular to L.

Jaxon Hamilton
2022-07-26
Answered

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Sandra Randall

Answered 2022-07-27
Author has **17** answers

Draw a straight line with a ruler, and label that line as L. Somewhere off that line, draw your point P. Then, draw a straight line through P onto L. If you have a protractor, you can measure that the angles on either side measure 90 degrees. By definition of perpendicular, all the angles must be right angles in order to be perpendicular. If you have access to the program Geometer's Sketch Pad, or something similar, it will also confirm that the line is perpendicular by confirming that the angles created are 90 degrees.

asked 2022-07-27

The medians of a triangle are the line segments from each vertex to the midpoint of the opposite side.Find the lengths of the medians of the trangle with vertices at A=(0,0), B=(6,0), and C= (4,4).

asked 2022-05-09

Suppose you have a pair of lines passing through origin, $a{x}^{2}+2hxy+b{y}^{2}=0$, how would you find the equation of pair of angle bisectors for this pair of lines. I can do this for 2 separate lines, but I am not able to figure it out for a pair of lines. Can someone please help.

asked 2022-05-10

Given: ABCD is a parallelogram,$\overline{AM},\overline{BN}$ angle bisectors,$DM=4\phantom{\rule{thinmathspace}{0ex}}\text{ft.}$, $MN=3\phantom{\rule{thinmathspace}{0ex}}\text{ft.}$Find: the perimeter of ABCD

asked 2022-06-21

The points (0,9),(12,0) and (0,0) create a right triangle. Find the equation of the angle bisectors for each of the three angles on the triangle.

I am unsure of how to find the equations. Any help will be greatly appreciated!

I am unsure of how to find the equations. Any help will be greatly appreciated!

asked 2022-06-21

Here are the five postulates:

1. Each pair of points can be joined by one and only one straight line segment.

2. Any straight line segment can be indefinitely extended in either direction.

3. There is exactly one circle of any given radius with any given center.

4. All right angles are congruent to one another.

5. If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if extended indefinitely, meet on that side on which the angles are less than two right angles.

Questions:

1. These to me sounds more like something that shouldn't require proving... does it?

2. Why is it important to stress things that are obvious? For example, what other answers can you get when extending a line segment other than it can be extended indefinitely in either direction?

3. Similarly, what space can allow two circle of the same radius and center to be not the same?

4. Saying all right angles are congruent ... isn't that the same as saying all 64.506 degree angles are congruent? Isn't it ANY angle are congruent if they are the same degrees measures from the same reference point (say x-axis)?

5. Why do we need the 5th postulate?

1. Each pair of points can be joined by one and only one straight line segment.

2. Any straight line segment can be indefinitely extended in either direction.

3. There is exactly one circle of any given radius with any given center.

4. All right angles are congruent to one another.

5. If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if extended indefinitely, meet on that side on which the angles are less than two right angles.

Questions:

1. These to me sounds more like something that shouldn't require proving... does it?

2. Why is it important to stress things that are obvious? For example, what other answers can you get when extending a line segment other than it can be extended indefinitely in either direction?

3. Similarly, what space can allow two circle of the same radius and center to be not the same?

4. Saying all right angles are congruent ... isn't that the same as saying all 64.506 degree angles are congruent? Isn't it ANY angle are congruent if they are the same degrees measures from the same reference point (say x-axis)?

5. Why do we need the 5th postulate?

asked 2022-05-07

Given rectangle ABCD with K the midpoint AD and $AD/AB=\sqrt{2}$ , find the angle between BK and diagonal AC.

asked 2022-07-29

Points P, Q, R, S, T, and U are all different points lying in the same plane. Points P, Q, andU lie on the same line. The line through points P and Q is perpendicular to the line through points R and S. The line through points R and S is perpendicular to the line through points T and U. Which of the following sets contains points that must lie on the same line?