In ΔABC, AD ⊥ BC and BE ⊥ AC. AD and BE intersect each other at F. If BF = AC, then the measure of ∠ABC is:
Show answer & explanation
Correct answer: C
Explanation
Correct Answer is option 3 i.e. 45°
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Concept |
Understanding |
Application |
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AA property: If 2 angles of 2 triangles are equal, they must be similar triangles. |
Given AD ⊥ BC and BE ⊥ AC BF = AC
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Here ∆AEF ~ ∆BDF (By AA) So, ∠DBF = ∠EAF Now, ∠DBF = ∠CAD and ∠BDF = ∠ADC Hence, ∆BDF ~ ∆ADC (By AA) BD/AD = DF/DC = BF/AC Since, BF = AC ⇒ BD = AD and DF = DC Hence, ∠ABD = ∠BAD = 45° |
