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Congruence Of Triangles

Question

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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

Solution

(a) SSS, as the sides of ΔABC are equal to the sides of ΔDEF.

(b) SAS, as two sides and the angle included between these sides of ΔPQR are equal to two sides and the angle included between these sides of ΔXYZ.

(c) ASA, as two angles and the side included between these angles of ΔLMN are equal to two angles and the side included between these angles of ΔGFH.

(d) RHS, as in the given two right-angled triangles, one side and the hypotenuse are respectively equal.

Some More Questions From Congruence of Triangles Chapter

Complete the following statements:
(a) Two line segments are congruent if .
(b) Among two congruent angles, one has a measure of 70°; the measure of the other angle is .
(c) When we write ∠A = ∠ B, we actually mean __.

Give any two real-life examples for congruent shapes.

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)

…

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

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