# Congruence of Triangles

**Exercise 1**

**1. ** Complete the following statements:

(a) Two lines segments are congruent if _____.

(b) Among two congruent angles, one has a measure of 70, the measure of other angle is _____.

(c) When we write ∠ A = ∠ B, we actually mean _____.

**2. **Give any two real time examples for congruent shapes.

**3. **If ΔABC ≅ ΔFED under the correspondence ABC ↔ FED, write all the corresponding congruent parts of the triangles.

**4. ** If ΔDEF ≅ ΔBCE, write the part(s) of ΔBCA that correspond to:

**Exercise 2**

**5. ** Which congruence criterion do you use in the following?

(a) Given: AC = DF, AB = DE, BC = EF

So ΔABC ≅ ΔDEF

(b) Given: RP = ZX, RQ = ZY, ∠ PQR = ∠ XYZ

So ΔPQR ≅ ΔXYZ

(c) Given ∠MLN = ∠FGH, ∠NML = ∠HFG, ML = FG

So ΔLMN ≅ ΔGEH

(d) Given: EB = BD, AE = CB, ∠ A = ∠ C = 90°

So ΔABE ≅ ΔCDB

**6.**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) ?

**7. ** You have to show that ΔAMP ≅ ΔAMQ. In the following proof, supply the missing reasons:

**8. ** 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?

**9.**In the figure, the two triangles are congruent. The corresponding parts are marked. We can write ΔRAT ≅ ?

**10. ** Complete the congruence statement:

**11. ** In a squad sheet, draw two triangles of equal area such that:

(i) The triangles are congruent.

(ii) The triangles are not congruent.

What can you say about their perimeters?

12. Draw a rough sketch to two triangles such that they have five pairs of congruent parts but still the triangles are not congruent.

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

**14. ** Explain, why ΔABC ≅ ΔFED.