1. Complete the following statements?
   a) Two line segments are congruent if _______.
   b) Among two congruent angles,one has a measure of 70⁰,the measure of the other angle is _____.
   c) When we write ∠ A = ∠ B ,we actually mean ________?

a)  They have the same length.
b)  70⁰
c) m∠A=m∠B

Give any two real life examples for congruent shapes.
i) Sheets of same letter pad
ii) Biscuits in the same packet.

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

If these triangles are congruent ,then the corresponding angles and sides will be equal to each other .
  ∠A↔∠F ,  ∠B↔∠E, ∠C↔∠D,

4. If ΔDEF ≅ ΔBCA, write the part(S) of ΔBCA that correspond to
(i) ∠C  (ii)  (iii) ∠F (iv)

(i) ∠C
(ii)
(iii) ∠A
(iv)

5. a) Given, AC = DF, AB = DE and BC = EF. Prove that  .

b)Given, PR=XZ, PQ=XY and ∠ RPQ=∠ZXY. Prove that .

a) The sides of ΔABC are equal to the sides of ΔDEF. Hence by SSS congruence criterion, .

             b)

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, by SAS congruence criterion  .

6. You want to show that .
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 ∠RTA=∠ENP 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 , then you need to show that 
    (i) ?  (ii) ? 
                    

(a) (i) AR = PE
      (ii) RT = EN
     (iii) AT = PN

    (b) (i) RT = EN
    (ii) PN = AT

    (c) (i)∠ ATR = ∠ PNE
         (ii)∠ RAT = ∠ EPN

7. You have to show that . In the following proof, supply the missing reasons.

	Steps		Reasons
(i)	PM=QM	(i)	____
(ii)	∠PMA =∠QMA	(ii)	_____
(iii)	AM = AN	(iii)	______
(iv)	ΔAMP ΔAMQ	(iv)	____

(i) Given
(ii) Given
(iv) common
(iv) by SAS criterion

8. In ΔABC, ∠ A=30⁰ , ∠B=40⁰ and ∠C=110^0.
    In ΔPQR, ∠ P=30⁰ , ∠Q=40⁰ and ∠R=110^0.
   A student says that ΔABC ≅ ΔPQR by AAA congruence criterion. Is it true? justify your answer.

 No.

There is no AAA congruency criterion. Even if all the angles of two triangles are same, it doesnt make them congruent as their sides may increase or decrease without disturbing the measures of the angles.

9. Observe the figure and prove that ΔRAT ≅ ΔWON.

   
It can be observed that
∠ RAT = ∠ WON
∠ ART = ∠OWN
AR = OW
∴ ΔRAT ≅ ΔWON, by ASA Criterion

10. Complete the congruence statement .
     ΔBCA  ≅  ?
     ΔQRS  ≅  ?
 
BC = BT (Given)
TA = CA (Given)
BA = BA (common)
∴ ΔBCA ≅ ΔBTA

Similarly,

PQ = RS
TQ = QS
PT = RQ
∴ ΔQRS ≅ ΔTPQ

11. If Δ ABC and ΔPQR are to be congruent, a) name one additional pair of corresponding parts,  b) what criterion did you use ?

a) BC = QR, b) ASA criterion

12. Explain why ΔABC ≅ ΔFED.
   

Given,

∠ABC = ∠FED →(1)
∠BAC = ∠EFD →(2)

The two angles of ΔABC are equal to the two respective angles of ΔFED.Also,the sum of all interior angles of a triangle is 180⁰
∴ the third angle of both triangles will also be equal in measure.
                  ∠BCA = ∠EDF →(3)
Also given,

                       BC = ED       →(4)
By using equation (1),(3) and (4), we obtain
                  ΔABC ≅ ΔFED (ASA Criterion)

13. State SSS congruence criterion.

Two triangles are congruent, if three sides of one triangle are equal to the three corresponding sides of the other triangle.