How to draw a triangle?
Watch the video
The construction of various triangles is a mandatory element of the school geometry course. For many, this task causes fear. But in fact, everything is quite simple. The rest of the article describes how to draw a triangle of any type using a compass and a ruler.
- acute angle;
- inscribed in a circle;
- described around the circumference.
Construction of an equilateral triangle
Equilateral is called a triangle, in which all sides are equal. Of all the types of triangles, draw equilateral the easiest.
- Using a ruler, draw one of the sides of a given length.
- Measure its length with a caliper.
- Place the compass point at one end of the line and draw a circle.
- Move the point to the other end of the segment and draw a circle.
- We got 2 points of intersection of circles. Combining any of them with the edges of the segment, we get an equilateral triangle.
Construction of an isosceles triangle
This type of triangles can be built on the base and sides.
An isosceles triangle is called, in which the two sides are equal. In order to draw an isosceles triangle according to these parameters, you must perform the following steps:
- With the help of a ruler set aside a segment equal in length to the base. We denote it by the letters AU.
- With a caliper measure the required length of the side.
- We draw from point A, and then from point C, a circle whose radius is equal to the length of the side.
- We get two points of intersection. Combining one of them with points A and C, we obtain the necessary triangle.
Construction of a right triangle
A triangle with one angle of a line is called rectangular. If we are given the legs and the hypotenuse, draw a right triangle is not difficult. It can be built on the leg and hypotenuse.
- Using the ruler draw the hypotenuse of a given length. We call this segment AB.
- Put the edge of a compass into point A and draw a semicircle, radiuswhich is slightly more than half a segment.
- Shift the compass point to point B and perform the same action.Our arcs intersect in two places. Connect these points. The point of intersection of this line and segment AB is its middle, point O.
- With the help of a compass draw a circle whose center is at the point O, and the radius is equal to the segment AO.
- From point A we make an arc compass, the radius of which is equal to the given leg. The point of intersection of the arc and the circle is the desired third vertex of the triangle. We connect it with points A and B. The task is completed.
Construction of a blunt-angled triangle on the corner and two adjacent sides
If one of the corners of a triangle is obtuse (more than 90 degrees), it is called obtuse. To draw an obtuse triangle using the specified parameters, do the following:
- With the help of a ruler, we postpone a segment equal to the length of one of the sides of the triangle. Denote it by the letters A and D.
- If the task has already drawn an angle, and you need to draw the same, then on its image to put two segments, both ends of which lie at the top of the corner, and the length is equal to the specified sides. Connect the resulting points. We have the desired triangle.
- To transfer it to your drawing, you need to measure the length of the third party.
Construction of an acute triangle
An acute triangle (all angles less than 90 degrees) is built on the same principle.
- Draw two circles. The center of one of them lies at point D, and the radius is equal to the length of the third side, while the second center is at point A, and the radius is equal to the length of the side specified in the task.
- Connect one of the intersection points of the circle with the points A and D. The sought triangle is constructed.
In order to draw a triangle in a circle, you need to remember the theorem, which says that the center of the circumscribed circle lies at the intersection of the middle perpendiculars:
- With a circular circle we draw two circles, the centers of which lie at different ends of a segment of one of the sides, and the radii (the same) are slightly largerhalf its length. Connect the intersection points of the circles. This will be our middle perpendicular.
- We build two middle perpendiculars to two any sides. The intersection point (let's call it O) is the center of the desired circumscribed circle. According to the axiom, two straight lines can have only one intersection point, so there is no need to draw all three perpendiculars.
- We measure with compasses the distance from point O to any of the vertices of the triangle and draw a circle. Task completed.
In an obtuse-angled triangle, the center of the circumscribed circle lies outside the triangle, and in a rectangular, in the middle of the hypotenuse.
Draw the described triangle
The described triangle is a triangle with a circle in its center touching all its sides. The center of the inscribed circle lies at the intersection of the bisectors. To build them you need:
- With an arbitrary radius we draw an arc whose center is one of the vertices of the triangle. The points of intersection of the arc with the sides are called P and M.
- With the same radius we draw two more arcs, with centers at points P and M. We connect the point of their intersection with the original vertex. Bisector built.
- Draw 2 bisector. The point of their intersection (we denote it by O) is the center of our future circle.
- In order to determine the radius of a circle, it is necessary to build a perpendicular from point O to any of the sides.
- With an arbitrary radius we draw an arc with center at point O so that it intersects the chosen side (let it be the side of the AU) in two places.
- With a radius of AO, we draw two circles with centers at points A and C. We connect the intersection points of the circles. The point of intersection of this line and the side of the AU (we denote it by E) is the desired perpendicular.
- We measure with a compass a piece of EO and draw an inscribed circle.
- This way you can draw the described triangle.