#### How to draw the Isosceles Triangles? Properties of Isosceles Triangle construction.

Isosceles Triangles Constructions

If we are given one angle of an isosceles triangle then we can alvvays calculate the other two angles. Given the vertical angle, we sublract it from 180° and divide the result by 2 to find the two base angles. Given a base angle, we multiply it by 2 and subtract the result from 180° to find the vertical angle.

So, if we are given any side and any angle of an isosceles triangle, then we can construct the triangle using the ASA method.

Also, if we are given a vertical side and the base of an isosceles triangle then, since the two vertical sides are equal, we can construct the triangle using the SSS method.

Example 1. Given one side and one angle

Construct an isosceles triangle in which the vertical angle is 50° and the base side is 6 cm

If we call the triangle ABC where A is the vertical angle then we must first calculate the base angles, mB and mC.

$\displaystyle m\overset{\wedge }{\mathop{B}}\,=m\overset{\wedge }{\mathop{C}}\,=\frac{1}{2}x\left( 180{}^\circ -50{}^\circ \right)=65{}^\circ$

We now have mB = 65°, a = 6 cm and mC = 65°. So we construct the triangle according to the ASA method.

Example 2, Given two sides

Construct an isosceles triangle in vvhich the base is and a vertical side is 5 cm

Since the other vertical side is also 5 cm we construct the triangle according to the SSS method.

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