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Question
Explain, why ΔABC ≅ ΔFED.
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Solution
Given that, ∠ABC = ∠FED (1)
∠BAC = ∠EFD (2)
The two angles of ΔABC are equal to the two respective angles of ΔFED. Also, the sum of all interior angles of a triangle is 180º. Therefore, third angle of both triangles will also be equal in measure.
∠BCA = ∠EDF (3)
Also, given that, BC = ED (4)
By using equation (1), (3), and (4), we obtain
ΔABC ≅ ΔFED (ASA criterion)
RELATED QUESTIONS
Line l is the bisector of an angle ∠A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ∠A (see the given figure). Show that:
- ΔAPB ≅ ΔAQB
- BP = BQ or B is equidistant from the arms of ∠A.
Which congruence criterion do you use in the following?
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RQ = ZY
∠PRQ = ∠XZY
So, ΔPQR ≅ ΔXYZ
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In ΔPQR, ∠P = 30°, ∠Q = 40° and ∠R = 110°
A student says that ΔABC ≅ ΔPQR by AAA congruence criterion. Is he justified? Why or why not?
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CD + DA + AB > BC
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Prove that: ΔAOD≅ ΔCOD
