Page 194 - ICSE Math 7

∴ perimeter of ∆ ABC = perimeter of ∆ PQR.

In (b), perimeter of ∆ RAT ≠ perimeter of ∆ COW.
Example 13: In the given figure, prove that ∆ AOC  ∆ BOD. C

Solution: In ∆ AOC and ∆ BOD

∠A = ∠B (given) B
A O
∠AOC = ∠BOD (vertically opposite angles)
∠C = ∠D (angle sum property)

 AC = BD (given) D

∴ ∆ AOC  ∆ BOD (by ASA congruency criterion)

EXERCISE

1. Examine whether ∆ DEF is congruent to ∆ PQR or not?

∆ DEF : ∠D = 100°, DE = 3 cm, ∠E = 60°
∆ PQR : ∠Q = 60°, PQ = 3 cm, ∠R = 20°
In case of congruency, mention the criterion.
2. State which of the following pairs of triangles are congruent. In case they are congruent, state
the criterion of congruency.

(a) (b)

(c) (d)

(e) (f)

3. State the correspondence between the parts if:
(a) ∆ PQR ≅ ∆ XYZ (b) ∆ OPT ≅ ∆ FUG
D C

4. In the adjoining figure, DC || AB, AD = BC. Prove using
the concept of congruent triangles that AE = BF.
A E F B
5. Draw a diagram for the following statements and prove the result.
(a) In an isosceles triangle, the median joining the vertex (formed by intersection of equal sides)
to the midpoint of opposite side is also an altitude.
(b) Any two altitudes of an equilateral triangle are congruent.

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