Page 190 - Start Up Mathematics_7

Two triangles are also congruent if two angles and a side of one A D
triangle are respectively equal to the two angles and a side of
the other triangle. This is known as AAS congruency criterion.
Because of angle sum property of triangle AAS leads to ASA
congruency criterion. B C E F

Example 12: In the given figures, measures of some parts are indicated. By applying ASA
congruence rule, state which pairs of triangles are congruent. In case of congruence,
write the result in symbolic form.

4.3 cm D D
A B P E
80° 40° 45° 120°

(a) (b) 5.2 cm 5.2 cm

40° 80°
C E 4.3 cm F 120° 45°
Q R F
D C
R M

(c) 60° 6 cm (d)

30° 60° 30° 40° 40°
P Q L 6.5 cm N 30° 30°
A B

Solution: (a) In ∆ ABC and ∆ FED (b) In ∆ PQR and ∆ FDE

∠A = ∠F (each 80°) ∠Q = ∠D (each 120°)
∠R = ∠E (each 45°)
AB = FE (each 4.3 cm)
∴ ∠P = ∠F
∠B = ∠E (each 40°) (by angle sum property of triangle)

∴ ∆ ABC  ∆ FED RP = EF (each 5.2 cm)
(by ASA congruence criterion) ∴ ∆ PQR  ∆ FDE

(by ASA congruence criterion)

(c) In ∆ RQP and ∆ LNM (d) In ∆ ABC and ∆ BAD
∠CAB = ∠DBA (each 30°)
∠R = ∠L (each 60°)

∠Q = ∠N (each 30°) AB = BA (common)
∠ABC = ∠BAD (each 70°)
but RQ ≠ LN
∴ ∆ ABC  ∆ BAD
∴ ∆ RQP ≅ ∆ LNM
(by ASA congruence criterion)
Example 13: Measurements of some parts of two triangles are given. Examine whether the two
triangles are congruent or not by ASA congruence rule. In case of congruence, write
it in symbolic form.

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