Constructing an Angle Bisector



the key points to an angle bisector is that it does almost lost dirt is that it does a couple things the first thing is it bisects the angle creating two congruent angles so if I have an angle that's in blue here and the red ray is my angle bisector then it has created two congruent angles so notice that this red is a rape so that's another key thing now it also could be a line segment if you're talking about something in a nice ah sleaze triangle perhaps perhaps so we could say or a line segment and every point along this bisector is the same distance from the two rays that make up the sides but how do we measure distance well the shortest distance from a point on this ray to a ray that forms the angle is along a perpendicular so if you're to construct the perpendicular from the angle bisector to a side and if you did that down here then you would say that these two segments are congruent so that's the key parts to an angle bisector is that bisects the angle creating two congruent angles that it is a liner or it is a ray or a line segment and that every point on this ray is the same distance measured along the perpendicular from the Rays that make up your angle but how do we actually construct them well to do that let's grab our compass and our straightedge and head over to this angle right here so we know that we're going to create a ray that creates two congruent angles so the first thing you're gonna do is you're gonna swing an arc just like if you were duplicating an angle so from the vertex I'm going to swing an arc so that I create two points of intersection now I want to create a point out here that is the same distance from these two points of intersection so if you want to you can change your company but you don't have to for the sake of argument I will and you're going to swing an arc from each of these end points so there's one arc from this intersection here's another point of intersection that I'm going to swing an arc from now this point right here is the same distance from both of these endpoints so I'm going to connect this point of intersection with my vertex thereby creating my angle bisector so I'm going to draw this connect my vertex and that point of intersection and what we've created are two congruent angles then when they sum you get the angle that you started with

How to construct angle of 90 degree using Compass



welcome to education channel this video I am going to explain you how to consider to nineteen ninety degrees using only compass how to construct 90 degrees angle with compass and explain first we'll take a line segment now at this point at this point I want exactly consider to a 90 degrees angle so what you take first this from this point any point this is an American construct 90 degrees so I'm going to concerts night right to say I mean 90 degrees line there's some reasonable radius so don't take more than a very small take some radius and this is a center point and drawn out actually 90 is off of the 180 right 180 divided by two is ninety if I can find out 180 degree point then I can buy 6 0 and 180 from here I draw a not without changing the radius previous how much until you drop how much radius you are drawn without changing this now me here cut this arc and again from this point became Amarok again from here one more on that means this is 60 degrees and this is 120 degrees and remaining is 180 degree now this is a zero point and this is 180 degree point right now 0 and 185 bisect then 90 will come need not to extend the line at this point I want know this is the a so at the point yeah I mean 90 degrees so from a troy log first 60 120 and 180 three arcs if I got now from 0 and this one zero and 180 I have to bisect so from zero just take more radius draw an arc a bow because I am visible again same radius from 180 mark because I'm bisecting zero and 180 so 90 we come the simple logic 0 arc and from our nadh on dry not with the same radius no wait they join the both points just to draw a line from the now this angle if you keep the point C so angle B is exactly 90 degrees so you can check with protractor I kept it so exactly 90 degrees so this is the way we can construct until 90 degrees at any point okay we'll check from this is right curves one more thing I'll show you one more example I would construct 90 degrees they said awesome so what we'll take from the center point we just draw an arc right with the same radius factor to us and from yeah so zero point and one negative point in extent zero and 180 so I need to bisect this now this is 180 point cut our kaboom and from here be same they both both six from the zero point and 180 point and then joy if we join the two points so this is the angle 90 so you can use any side any way to not only these any line segment is given at any point we can construct 90 degrees using compass

Constructing an Altitude of a Triangle



welcome to a lesson on how to construct an altitude of a triangle an altitude is a line segment from a vertex that is perpendicular to the opposite side so this red segment is an altitude because it's a line segment from this vertex to the opposite side and is perpendicular to the opposite side each triangle has three altitudes from each of our techs and the point of concurrency is called the orthocenter so here 0.0 is the point of concurrency with a point of intersection of the three altitudes and this is called the orthocenter now we're going to take a look at constructing an altitude for an acute triangle in an up to triangle and for these constructions we're going to need a compass and a straightedge so for this example we have an acute triangle and we'll construct the altitude from this vertex so the first step is to put the point of the compass on this vertex and open it far enough so that when we swing an arc it will intersect the opposite side in two points and if you want you can extend this side of the triangle so in this example if we swing an arc that look similar to this notice how it intersects the opposite side in two points we have a point of intersection here and we have another point of intersection here now we're going to take the compass and put the point on one of the points of intersection and then open it so that it's more than half the distance from this intersection point to this intersection point and once we do that we'll swing an arc above and below this side of the triangle so it might look something like this we want to make sure we swing them so that they would extend past what we think would be the midpoint of the segment between these two points of intersection and now without adjusting the compass we'll put the point on the other point of intersection here and then swing another arc above and below this side of the triangle and those arcs might look something like this now we're going to take our straightedge and line up the intersection of the arcs here and here with this vertex and this should be our altitude so this red segment would be our altitude because it connects this vertex to the opposite side and is perpendicular to that opposite side now let's take a look at the construction when we have an obtuse triangle if we want to construct the altitude from this vertex here to the opposite side notice how we're going to have to extend the opposite side in order to make a segment that's perpendicular to that side so with our straightedge we'll go ahead and extend this side and then we'll perform the same procedure we'll take the point of our compass put it here on the vertex and then we'll open up the compass large enough so that when we swing an arc it will intersect the opposite side in two points and when we swing an arc it might look something like this and notice how it intersects the opposite side in two points we have one point of intersection here and one point of intersection here next we'll take the compass and put the point on one of the points of intersection and then open up the compass so that extends past half the distance from these two points of intersection and then swing an arc above and below this side of the triangle so if we put the point on this point of intersection and swing an arc above and below it might look something like this and then without adjusting the compass we'll put the point on the other point of intersection and do the same swing an arc above and below the side of the triangle so it might look something like this now if we line up the points of intersection of these arcs with this vertex it should form our altitude so with a straight edge we'll line these three points up they should be linear and construct our altitude and notice how this segment is perpendicular to the opposite side here therefore this should be our altitude I hope you found this helpful you