OD bisects angle AOB. DA and DB are perpendicular from point D on the rays OA and OB . Show that DA is congruent with DB
Answers
If OD bisects angle AOB and DA & DB are perpendicular from point D on the rays OA and OB, then DA is congruent with DB by C.P.C.T.
Step-by-step explanation:
Referring to the figure attached below, we have
∠AOD = ∠BOD …… (i) ….. [as OD bisects ∠AOB (given)]
∠OAD = ∠OBD = 90° …… (ii) ……. [DA and DB are perpendicular from point D on rays OA & OB (given)]
Now, let’s consider ∆ADO & ∆BDO, we have
∠AOD = ∠BOD ….. [from (i)]
OD = OD …… [common side to both the triangles]
∠OAD = ∠OBD …… [from (ii)]
∴ By ASA congruence, ∆ADO ≅ ∆BDO
We know that if two or more triangles are congruent to each other, then all of their corresponding angles and sides are congruent as well. This property is known as Corresponding Parts of Congruent Triangles which is abbreviated as “C.P.C.T”.
∴ DA = DB
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