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4. Make a pair of ΔPQR and ΔSTU from glazed paper such that QR = TU, ∠Q = ∠T and ∠R = ∠U
and cut them out. (see Fig. 14.4)

5. Make two right angle triangles such that ΔXVZ and ΔLMN from glazed paper such that YZ = MN,
XZ = LN and ∠X = ∠L = 90°. (see Fig. 14.5)

Demonstration

1. Superpose ΔABC on ΔDEF completely only under the correspondence A ↔ D, B ↔ E and C ↔
F. See that ΔABC covers ΔDEF completely.
Hence, ΔABC ≅ ΔDEF
if AB = DE
BC = EF
and AC = DF
which is the SSS criterion for congruency.
2. Similarly, superpose ΔGHI on ΔJKL completely only under the correspondence G ↔ J, H ↔ K
and I ↔ L. See that ΔGHI covers ΔJKL completely.
Hence, ΔGHI ≅ ΔJKL
if GH = JK
∠G = ∠J
and Gl = JL
which is the SAS criterion for congruency.
3. Similarly, superpose ΔPQR on ΔSTU only under the correspondence P ↔ S, Q ↔ T and R ↔ U.
See that ΔPQR covers ΔSTU completely.
Hence, ΔPQR ≅ ΔSTU
if ∠Q = ∠T
QR = TU
and ∠R = ∠U
which is the ASA criterion for congruency,
4. Similarly, superpose ΔYXZ on ΔMLN only under the correspondence Y ↔ M, X ↔ L and Z ↔ N.
See that ΔYXZ covers ΔMLN completely.
Hence, ΔYXZ ≅ ΔMLN
if ∠X = ∠L = 90°