- #1
mathlearn
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Construct vertex D of an acute angled triangle
In summary, to find the location of point $D$ so that both triangles have the same area, draw a parallel line through $C$ to the base $AB$ and mark $D$ on this line so that $CA=CD$. This ensures that the heights of both triangles are equal and therefore, the area will be equal.
- #2
Evgeny.Makarov
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You know the formula for the area of a triangle. Why don't you describe your ideas on the location of $D$?
- #3
mathlearn
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:) Both the triangles should be on the same base and between same pair of parallel lines
I am not sure whether it correct but here are my ideas
I think It has got to do something with parallelograms, I guess?
Many Thanks :)
I am not sure whether it correct but here are my ideas
I think It has got to do something with parallelograms, I guess?
Many Thanks :)
- #4
Evgeny.Makarov
Gold Member
MHB
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Yes, but the problem statement also stipulates that $CA=CD$. So you should draw the line through $C$ that is parallel to $AB$ and then mark $D$ on that line so that $CA=CD$. To draw a parallel line through $C$, see here.mathlearn said:
- #5
HallsofIvy
Science Advisor
Homework Helper
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It has to do with the fact that the area of a triangle is "(1/2) base times height". Since the two triangles will have the same base, their heights must also be the same. That is the reason for drawing the line, through C, parallel to AB. The further condition is that "CA= CD". Set one leg of a pair of compasses at C, set the other on A, and draw an arc with center at C and radius CA. D is where the line and arc intersect.
- #6
mathlearn
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Correct ?
- #7
Evgeny.Makarov
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MHB
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Yes, it's correct.
1. How do I construct vertex D of an acute angled triangle?
To construct vertex D of an acute angled triangle, you will need to use a compass and a straightedge. Begin by drawing two sides of the triangle, making sure they are not parallel. Then, use the compass to measure the length of the third side from one of the existing vertices. Draw an arc from the other vertex that intersects with the first arc. The intersection of these two arcs will be vertex D.
2. What is an acute angled triangle?
An acute angled triangle is a type of triangle that has all three angles measuring less than 90 degrees. It is also known as a acute triangle or a sharp triangle. In an acute angled triangle, the sides opposite the acute angles are the shortest sides.
3. Why is it important to construct vertex D of an acute angled triangle accurately?
It is important to construct vertex D of an acute angled triangle accurately because it ensures that the triangle is a true acute angled triangle. If vertex D is not constructed correctly, the triangle may end up being a right triangle or an obtuse triangle, which will change the properties and measurements of the triangle.
4. Can I construct vertex D of an acute angled triangle without a compass?
No, you cannot construct vertex D of an acute angled triangle without a compass. The compass is used to measure and draw the arcs needed for the construction. Without a compass, it would be difficult to accurately measure the length of the third side and draw the intersecting arcs.
5. What is the difference between constructing vertex D of an acute angled triangle and constructing other types of triangles?
The process of constructing vertex D of an acute angled triangle is similar to constructing other types of triangles, such as equilateral or isosceles triangles. However, the main difference is that in an acute angled triangle, the angles are all less than 90 degrees, so the compass must be set to a smaller radius to create the intersecting arcs. Additionally, the placement of the compass and the arcs may vary depending on the given measurements and angles of the triangle.
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