Question
In the isosceles ΔABC with AB = AC. E and O are the midpoints of AB and AC respectively. 2OD = DE and ∠OCD = 70o. Prove using congruency that ∠EAO = 70o. [4 MARKS]
Answer:
:
Steps: 2 Marks
Proof: 2 Marks
In ΔABC,
OD + OE = DE
Multiplying both sides with 2:
2OD + 2OE = 2DE
DE + 2OE = 2DE (2OD = DE; given in question)
2OE = DE
So, OD = OE -------------- (1)
InΔAOEandΔDOC,
OD = OE [From (1)]
∠AOE = ∠DOC [Vertically Opposite Angles]
AO = OC [O is the mid-point of AC]
ΔAOE≅ΔDOC [By SAS condition]
Hence, ∠EAO= ∠OCD= 70o [Corresponding parts of corresponding triangles]
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:
Steps: 2 Marks
Proof: 2 Marks
In ΔABC,
OD + OE = DE
Multiplying both sides with 2:
2OD + 2OE = 2DE
DE + 2OE = 2DE (2OD = DE; given in question)
2OE = DE
So, OD = OE -------------- (1)
InΔAOEandΔDOC,
OD = OE [From (1)]
∠AOE = ∠DOC [Vertically Opposite Angles]
AO = OC [O is the mid-point of AC]
ΔAOE≅ΔDOC [By SAS condition]
Hence, ∠EAO= ∠OCD= 70o [Corresponding parts of corresponding triangles]
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