Congruence of Triangles
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:
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.