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Mobile App Chapter 2: Q8. (page 65)
Give a plan for the following proof.
Given:∠1 is supplementary to∠3;∠2 is supplementary to∠3.
Prove:
Short Answer
The line j is perpendicular to line k.
Step by step solution
Step 1. Observe the given diagram.
The given diagram is:
Step 2. Definition of supplementary angles.
The supplementary angles are the angles whose sum is 180°.
Step 3. Write the proof of the statement j⊥k.
∠1 is supplementary to∠3.
Therefore, the sum of angles ∠1 and ∠3 is 180°.
That implies,
∠2 is supplementary to∠3.
Therefore, the sum of angles ∠2 and ∠3 is 180°.
That implies,
From the equations (1) and (2), it is obtained that:
That implies .
From the given diagram it can be noticed that angles ∠1 and ∠2 are the adjacent angles.
Therefore, angles ∠1 and ∠2 are the adjacent congruent angles.
Now by using the theorem of the converse of perpendicular lines it can be said that if the angles ∠1 and ∠2 are the adjacent congruent angles, then the lines j and k are perpendiculars.
That implies .
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