Chapter 2: Q7. (page 62)
Describe your plan for proving the following. You don’t need to give all the details.
Given:
Prove:
Short Answer
As, ,therefore the angles∠2and∠3are congruent angles.
Therefore, .
From the diagram it can be noticed that the angles∠2 and∠3 are the vertical angles.
Therefore, by using the theorem of vertical angles it can be said that the angles ∠1 and∠2are the congruent angles.
That implies,
From the diagram it can also be noticed that the angles∠3 and∠4are the vertical angles.
Therefore, by using the theorem of vertical angles it can be said that the angles ∠3 and∠4 are the congruent angles.
That implies,
By using the equations (1), (2) and (3):
Therefore, the angles∠1 and∠4have same measure.
Therefore, the angles∠1 and∠4 are the congruent angles.
That implies, .