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## High school geometry

### Course: High school geometry>Unit 3

Lesson 8: Constructing lines & angles

# Geometric constructions: angle bisector

Sal constructs a line that bisects a given angle using compass and straightedge. Created by Sal Khan.

## Want to join the conversation?

• He says that we know the two triangles are congruent, but he doesn't prove it. How do we know? • I have been watching a couple of videos about trisecting arbitrary angles, using only an unmarked straightedge and compass. It is said to be impossible, because apparently Euclid said so.

But the girl in this video https://www.youtube.com/watch?v=XZPY86eo3XU is doing exactly that. She uses an unmarked straightedge and compass to trisect an angle. Nothing else.

Now on the wikipedia page it says the following, and I quote: "Angle trisection is a classical problem of compass and straightedge constructions of ancient Greek mathematics. It concerns construction of an angle equal to one third of a given arbitrary angle, using only two tools: an unmarked straightedge and a compass.

The problem as stated is impossible to solve for arbitrary angles, as proved by Pierre Wantzel in 1837. However, although there is no way to trisect an angle in general with just a compass and a straightedge, some special angles can be trisected. For example, it is relatively straightforward to trisect a right angle (that is, to construct an angle of measure 30 degrees).

It is possible to trisect an arbitrary angle by using tools other than straightedge and compass.
For example, neusis construction, also known to ancient Greeks, involves simultaneous sliding and rotation of a marked straightedge, which cannot be achieved with the original tools" end quote.

Note, a marked straightedge, like a ruler or something. She uses a neusis construction with an unmarked straightedge and compass.

Has she nailed it? If not, why not? She fullfills the requirement exactly. She trisects arbitrary angles using only a unmarked straightedge and compass using a neusis construction. How can this possibly not be a total win. XD • No, she has not. The problem require constructing it with only the straightedge and compass. Any other devices or constructions used are not allowed.

The neusis requires marking of the straight edge. We can't know that for these problems. It's meant to be a way to make lines. In general, if the method used needs something else other than
: a way to make a straight line
: a way to make a circle of any size

it is not allowed.
• Hey Sal, I loved your video but can you put some practice questions? It would really help, the video was awesome and I understood it! • angle 75
How can we draw angle 75 with a compass • So you could use a 90 degree angle and a 15 degree angle, so the 3rd angle would be 75 degrees. To get the 90, use a right triangle, and to get the 15, use an equilateral triangle, bisect the 60 degree in half, and then the 30 degree in half to get the 15 degree angle. But it's a pretty complex shape involving both a right triangle and an equilateral triangle combined. (Same answer as above)
• Sometimes, the three circle point does not work for an angle because the points are not able to intersect the same circle. How do you find the angle bisector in this case? • For a triangle, what is an angle bisector used to find? • Is the angle bisector also the side bisector? And also is the angle bisector always perpendicular to the side opposite the angle? Pls help.
(1 vote) • Question 1:
No, unless you have equilateral or isosceles triangle.
actually name of side bisector is median it equally divides side into two parts.

Question 2:
Also No, unless you have equilateral or isosceles triangle.

*in isosceles triangle it is only true if you construct
bisector from not equal angles. so if isosceles triangle has angles: 30, 30 and 120. bisector will be median and also a perpendicular if you construct it from 120 degree angle.   