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How To Solve Geometry Problems?

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Geometrical problems in mathematics are basically those which are related to geometrical shapes like Triangles, circles, quadrilaterals etc. To solve these problems we have well – defined theorems and formulas. Let us see how to solve Geometry problems with the help of examples.

Example 1: In the given triangle we have the measure of angle 'C' as 800. Find the measure of angles x and y, if triangle ABC is an Isosceles Triangle?



Solution: In the given triangle ABC we have two equal sides AC and AB [because the triangle is isosceles]. One angle ∠C is 80 degrees. As the two sides are equal, the angles opposite to them will also be equal and so ∠B = ∠C = 800. Now we are just left with one angle unknown.

 

Using the angle sum property of the triangles we can write:

A + ∠B + ∠C = 1800,

Substituting the values of ∠B and ∠C in the above equation we get:

x + 80 + 80 = 180,

or x = 180 – 160,

or x = 200,

Let us consider one more example:

Example 2: Suppose we are having a triangle whose sides are given as follows: PQ = 4 x, PR = 12 and RQ = 4 y. Find the value of x and y for which the sum of two sides PQ and QR is equal to the third side and also PQ = QR?




Solution: In the given triangle PQR according to the given conditions we can write:

 

PQ = QR,

Or 4 x = 4 y ….......equation 1

Also we have: PQ + QR = PR,

Or 4 x + 4 y = 12 …........equation 2

Now we have two equations and by solving them we can get the value of x and y as follows:

x = y = 12/8.