Congruence of Triangles

Explain, why

ΔABC ≅ ΔFED

If ΔABC and ΔPQR are to be congruent, name one additional pair of corresponding parts. What criterion did you use?

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?

Complete the congruence statement:

ΔBCA ≅?

ΔQRS ≅?

In the figure, the two triangles are congruent.

The corresponding parts are marked. We can write ΔRAT ≅ ?

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?

You have to show that ΔAMP ≅ AMQ.

In the following proof, supply the missing reasons.

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) ?

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

Which congruence criterion do you use in the following?

(a) Given: AC = DF

AB = DE

BC = EF

So, ΔABC ≅ ΔDEF

If ΔDEF ≅ ΔBCA, write the part(s) of ΔBCA that correspond to

(i) ∠E (ii)  (iii) ∠F (iv) 

If ΔABC ≅ ΔFED under the correspondence ABC ↆFED, write all the Corresponding congruent parts of the triangles.

Give any two real-life examples for congruent shapes.

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 __________.