1@ Soham : I dont think there was any SSA Congruency Criterion for triangles...was there ? [7]
12 Answers
1ΔABC ~ ΔEFD (AA Similarity)
So,
LF=LB=101°
and
LE=LA=30°
LF - LE = 101° - 30° = 71°
36But how can u make both of them similar...??
Do they look similar?
i don't think so.....!!
This problem is that that simple as u r taking it to be..
Theres a short-long thing inside it... which is gonna explore a big thing...!!
Which is 'a must know' but we dunno...!! :D
11
From THE SSA rule....ABC is CONGRUENT.to DEF..(the image is not right...but it may be assumed).
then...ang.F=ang C
ang E= ang A
Ang f-Ang E=101°-30°=71°
11rotate 1st triangle such that C coincides with D, A with E and B with F
so angle A = angle E = 30
F = 180 - 49 - 30
so F - E = 180 - 49 - 60 = 71
1well as the question cant be directly done by congruence and similarity (i mean you have to make some constructions which make such an easy question tougher) i present my trigonometry solution.
Firsdt of all angle ABC = 101°
using Sine rule in triangle ABC we get
sin49AB = sin 101AC........(1)
using Sine rule in triangle DEF we get
sin49EF = sin DFEDE............(2)
As DE= AB , (1) =(2)
from which we get
DEF = 101
and then DFE= 30 ( by angle sum property)
therfore LF - LE = 71°
:)
36@every1 - i said naa... therez a small but big thing to be revealed...
generally we all know only five criterions for congruency of triangles...
1. SAS
2. SSS
3. AAS
4. ASA
5. RHS
but in any of my 'upto 10th' level book i haven't found any criterion
like 'SSA' though there's a proof for it...
In the given triangles ABC and DEF we have been given that,
AB = DE , AC = DF and, LC = LF
Now, to prove, [ABC] = [DEF]
Now, we drop perpendiculars from A and D on BC at EF at M and N respectively...
Now, from triangles AMC and DNF we have,
LAMC = LDNF , AC = DF and LACM = LDFN
thus, [AMC] = [DNF] by AAS criterion..
=> AM = DN (c.p.c.t)
Again, in triangle AMB and DNE we have,
LAMB = LDNE = 900
AM = DN and AB = DE
Thus, [AMB] = [DNE] ..... by RHS criterion...
Thus, [AMC] + [AMB] = [DNF] + [DNE]
=> [ABC] = [DEF] proved...
Hence, SSA is in a crition for congruency of triangles..
Do remember it as well... :D
Be true!! Did u know that?
But why aren't we taught this...??
vote : ...... not lol
36so clearly,
/\ BAC ≡ /\ FED [by SSA - criterion]
Thus, LF = LB and LE = LA
i.e., LF = 180° - (30° + 49°) = 180° - 79° = 101°
And, LE = 30°
And hence, LF - LE = 101° - 30° = 71° Ans.
36nopes... i don't think so...!!
There is no such problem in NCERT... i guess...!!
The only thing which can kill such problems is the concept of
SSA or at last contruction... like drawing a perendicular nd all...!!