Sponsor Area
Congruence Of Triangles
In ΔABC, ∠A = 30°, ∠B = 40° and ∠C = 110°
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?
No. This property represents that these triangles have their respective angles of equal measure. However, this gives no information about their sides. The sides of these triangles have a ratio somewhat different than 1:1. Therefore, AAA property does not prove the two triangles congruent.
Some More Questions From Congruence of Triangles Chapter
Which congruence criterion do you use in the following?
(a) Given: AC = DF
AB = DE
BC = EF
So, ΔABC ≅ ΔDEF
(b) Given: ZX = RP
RQ = ZY
∠PRQ = ∠XZY
So, ΔPQR ≅ ΔXYZ
(c) Given: ∠MLN = ∠FGH
∠NML = ∠GFH
ML = FG
So, ΔLMN ≅ ΔGFH
(d) Given: EB = DB
AE = BC
∠A = ∠C = 90°
So, ΔABE ≅ ΔCDB
You want to show that ΔART ≅ ΔPEN,
(a) If you have to use SSS criterion, then you need to show
(i) AR = (ii) RT = (iii) AT =
(b) If it is given that ∠T = ∠N and you are to use SAS criterion, you need to have
(i) RT = and (ii) PN =
(c) If it is given that AT = PN and you are to use ASA criterion, you need to have
(i) ? (ii) ?
You have to show that ΔAMP ≅ AMQ.
In the following proof, supply the missing reasons.
–
Steps
–
Reasons
(i)
PM = QM
(i)
…
(ii)
∠PMA = ∠QMA
(ii)
…
(iii)
AM = AM
(iii)
…
(iv)
ΔAMP ≅ ΔAMQ
(iv)
…
–
Steps
–
Reasons
(i)
PM = QM
(i)
…
(ii)
∠PMA = ∠QMA
(ii)
…
(iii)
AM = AM
(iii)
…
(iv)
ΔAMP ≅ ΔAMQ
(iv)
…
In ΔABC, ∠A = 30°, ∠B = 40° and ∠C = 110°
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?
In a squared sheet, draw two triangles of equal areas such that
(i) The triangles are congruent.
(ii) The triangles are not congruent.
What can you say about their perimeters?
Explain, why
ΔABC ≅ ΔFED
Sponsor Area
Mock Test Series
Mock Test Series