Question
(a) Show with an example that two triangles can't be congruent using AAA criterion.
(b) Which congruence criterion will you use in the following?
Given: AC = DF
AB = DE
BC = EF
So, ΔABC ≅ ΔDEF
[3 MARKS]
(b) Which congruence criterion will you use in the following?
Given: AC = DF
AB = DE
BC = EF
So, ΔABC ≅ ΔDEF
[3 MARKS]
Answer:
:
(a) Proof: 2 Marks
(b) Answer: 1 Mark
(a)Consider the two triangles :
In the two triangles,
∠ABC = ∠PQR
∠BAC = ∠QPR
∠ACB = ∠PRQ
But clearly, ΔABC is not congruent to ΔPQR.
As the sides of triangle are not equal.
Thus, AAA cannot be a congruence condition.
It actually tells thatthe two triangles are similar, but not congruent.
(b) Since, the three sides of the first triangle is equal to the corresponding three sides of the second triangle, bySSScongruence criterion ΔABCis congruent to ΔDEF.
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:
(a) Proof: 2 Marks
(b) Answer: 1 Mark
(a)Consider the two triangles :
In the two triangles,
∠ABC = ∠PQR
∠BAC = ∠QPR
∠ACB = ∠PRQ
But clearly, ΔABC is not congruent to ΔPQR.
As the sides of triangle are not equal.
Thus, AAA cannot be a congruence condition.
It actually tells thatthe two triangles are similar, but not congruent.
(b) Since, the three sides of the first triangle is equal to the corresponding three sides of the second triangle, bySSScongruence criterion ΔABCis congruent to ΔDEF.
Was this answer helpful ?
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