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Construction of Triangles
Here we will learn to construct different types of triangles.
Construction of Equilateral Triangle:
We can draw an equilateral triangle of the given length as given below.
Step I: First, we draw a base line segment BC of the given length.
Step II: We place pointed end of the compass on the end point B of line segment and cut an arc with the given length as shown in figure.
Step III: We place the same end of the compass on the end point C of line segment and cut an arc with the same length in such a way that arcs intersect at a fixed point, say A.
Step IV: Now we join this fixed point A to the end points B and C of the line segments to form the required equilateral triangle.
∆ ABC has all the sides equal (AB = BC = AC).
Construction of Isosceles Triangle:
We follow the following steps to draw an isosceles triangle.
Step I: First, we draw a base line segment QR of the given length.
Step II: We cut two arcs with the given length from the points Q and R, so that they cut at a fixed point P.
Step III: We join points P and Q and points P and R to form the required isosceles triangle. ∆PQR has opposite sides equal. (PQ = PR)
Construction of Scalene Triangle:
We follow the following steps to draw a triangle.
Step I: We draw a base line segment NP of the given length.
Step II: We cut two arcs with given lengths from the points N and P, so that they intersect at point M.
Step III: Now, we join points M and N and points M and P to form the required scalene triangle. ∆ MNP has all the sides of different lengths.
A. When two sides and one angle formed by these sides are given.
Suppose, we have to construct a triangle TLK having the base side LK = 5 cm, side TL = 3 cm and ∠L = 45°.
Step I: First, we draw the base side LK of 5 cm.
Step II: Now, we form an angle L of 45° at the point L on the side LK with the help of a protractor.
Step III: Now we cut off the line segment LT of the length 3 cm from the side.
Step IV: We join points T and K to get the third side TK of the ∆ TLK.
So, ∆ TLK is the required angle.
B. When two angles and one side are given.
Suppose we have to construct a triangle XYZ having the base side YZ, 4.5 cm, angle Y, 40° and angle Z, 65°.
Step I: First we draw the base side YZ of 4.5 cm.
Step II: Now we form an angle Y of 40° on point Y on YZ with the help of a protractor.
Step III: Similarly, we form an angle Z of 65° on point Z on YZ with the help of a protractor.
Step IV: The sides, other than the base side, intersect at a point X. We join points X and Y and X and Z to form the required ∆ XYZ.
5th Grade Math Problems
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