Math Guide

Geometry Proofs worksheets

Geometry plays an important role in mathematics. Geometry is broadly classified into analytical and practical geometry. In proof, the condition should be solved analytically to show the given condition should be always true, the condition must be true under any circumstances. There are some predefined geometry theorems to show the given condition as a true statement. Let us discuss some geometry proofsworksheets.



Theorem 1 (geometry proofs worksheets):


Angles at a point add to 360o

Anglesatapointaddto360degree


Proof

In the above figure, the angles make up a full turn, and the sum of all the angles is 360o , so

a + b + c + d + e = 360o

This will fit for any number of angles. We are here proved by using five angles


Theorem 2 (geometry proofs worksheets):

The angle on a straight line is 180o.


Theangleonastraightline


Proof:

In the above figure, a and b are angles at a given point both are on the same vertex. So that a + b = 360o, by Theorem 1.

But a = b, so a + a = 360 degrees or 2a = 360 degrees, which gives

a = 180o.


Theorem 3 (geometry proofs worksheets):


The sum of angles on a straight line is 180

   Thesumofanglesonastraightlineis180

Proof:

In the above figure, both a and b are angles on a straight line and on a single vertex, so a+ b = 180o by theorem 2


Theorem 4 (geometry proofs worksheets):

Vertically opposite angles are equal

Verticallyoppositeanglesareequal

Proof:

In the above figure, angles a and b make up a straight line.

So, a + b = 180o, by theorem 2.

Angles a and c makes a straight line.

a + c = 180o, by theorem 2

so a + b = a + c

Subtracting a from both sides we get, b = c.


The perpendicular opposite angles b and c are equal.

Similarly,

a + b = 180o (angles on a straight line)

d + b = 180o (angles on a straight line)

so, a + b = d + b

Subtracting b from both sides we get, a = d.