Mathematics
In the adjoining figure, AB = AC and AD is median of △ABC, then ∠ADC is equal to
60°
120°
90°
75°
Answer
In △ADB and △ADC,
Given,
AB = AC (Given)
BD = DC (Given)
AD = AD (Common)
Hence, △ADB ≅ △ADC by SSS axiom.
We know that corresponding parts of congruent triangle are equal.
∴ ∠ADB = ∠ADC = x.
From figure,
⇒ ∠ADB + ∠ADC = 180°
⇒ x + x = 180°
⇒ 2x = 180°
⇒ x = 90°
∴ ∠ADC = 90°.
Hence, Option 3 is the correct option.
Related Questions
In the adjoining figure, AB ⊥ BE and FE ⊥ BE. If AB = FE and BC = DE, then
△ABD ≅ △EFC
△ABD ≅ △FEC
△ABD ≅ △ECF
△ABD ≅ △CEF
In the adjoining figure, AC = BD. If ∠CAB = ∠DBA, then ∠ACB is equal to
∠BAD
∠ABC
∠ABD
∠BDA
In the adjoining figure, O is the mid-point of AB. If ∠ACO = ∠BDO, then ∠OAC is equal to
∠OCA
∠ODB
∠OBD
∠BOD
In the adjoining figure, AB = FC, EF = BD and ∠AFE = ∠CBD. Then the rule by which △AFE ≅ △CBD is
SAS
ASA
SSS
AAS
