Euclidean Geometry

Geo means “earth” and metron  means “measurement”. ”Euclid, a distinguished Greek mathematician, called the father of geometry. A point is used to represent a position in space. A plane to be a surface extending infinitely in every directions such that all points lying on the line joining any two points on the surface. The euclidean geometry example problems and practice problems are given below.
Example Problems - Euclidean Geometry:

Example problem 1:

Can the following angles are triangle or not?

(a) 50° , 70°, 60° (b) 40°, 80°, 70°

Solution :
(a) The sum of the measure of the three angles is
50° + 70° + 60° = 180°
Therefore 50°, 70°, 60° can be the measure of the angles of a triangle.
(b) The sum of the measure of the three angles is
40° + 80° + 70° = 190°.
But the sum of the measure of the angles of a triangle is 180°.
Therefore 40°, 80°, 70° cannot be the measures of the angles of a triangle.

Example problem 2:

Find the supplementary angle of 95°

Solution:

The supplementary angle of 95° = 180° – 95° = 85°.

Example problem 3:

The lengths of two sides of right triangles are 6cm and 8cm. Find its hypotenuses.

Solution:

AC = 6 cm
BC = 8 cm
AB =?
AB2 = 62+ 82
= 36 + 64
AB2 = 100
AB = √100 = 10

Thus, the hypotenuses are 10 cms in length.
Practice Problems - Euclidean Geometry:

Practice problem 1:

Two angles of a triangle are of measures 52°and 78°. Find the measure of the third angle.

Ans: 50

Practice problem 2:

Find the angles in each of the following:
(i) The angles are supplementary and the larger angles are twice the small.
(ii) The angles are complementary and the larger is 20° more than the other

Ans:    1. smaller angle = 60°, larger angle = 120°.

2. smaller angle = 35°, larger angle =  55°.