If one of the four angles formed by two intersecting lines is a right angle, then each of the four angles is a right angle.
This statement is (True/False).
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Let us try to visualize the given statement using a diagram. Given :––––––––– One angle is a right angle. ∠AOB and ∠BOC form a linear pair.
Hence, sum of their measures must equal 180o. ∵m∠AOB=90o ∴m∠BOC=180o−90o=90o
Here, we have two pairs of vertical angles: ∙∠AOB and ∠COD ∙∠BOC and ∠DOA
Vertical Angles Theorem states that vertical angles are always congruent (equal in measure). ∴∠AOB = ∠COD and ∠BOC = ∠DOA
But we already have, m∠AOB=m∠BOC=90o ⇒m∠COD=m∠DOA=90o