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.