Page 189 - ICSE Math 7

Try This

State True or False.
(a) Two circles with equal radii are congruent.
(b) Two squares are congruent if a side of one square is equal to a side of the other.
(c) Two rhombuses are congruent if a side of one rhombus is equal to a side of the other.
(d) Two rectangles having same lengths and breadths may not be congruent.

Example 2: Give any two real-life examples of congruent shapes.
Solution: The two real-life examples of congruent shapes are:
(a) Two postcards (b) Maps of a country drawn on the same scale

Example 3: If ∆ ABC ≅ ∆ FDE under the correspondence ABC A F
↔ FDE, write all the corresponding congruent
parts of the triangles.
Solution: AB ↔ FD, BC ↔ DE, CA ↔ EF, ∠A ↔ ∠F,
∠B ↔ ∠D, ∠C ↔ ∠E B D

Conditions for congruency of two triangles C E
We know that two triangles are congruent if all the six parts, i.e., three sides and three angles of one
triangle are equal to the corresponding six parts of the other triangle. But in order to prove that two
triangles are congruent, there is no need to show equality of all the six corresponding parts. It is
sufficient to verify one of the following conditions or criterions:

Case I: Side-side-side (SSS) condition
If the three sides of one triangle are equal to the C R
corresponding three sides of the other triangle, then two
triangles are congruent.
Draw a ∆ ABC in which AB = 5 cm, BC = 6 cm, 7 cm 6 cm 7 cm 6 cm
CA = 7 cm. Draw another ∆ PQR with PQ = 5 cm,
QR = 6 cm, RP = 7 cm. A 5 cm B P 5 cm Q
Now trace a copy of ∆ ABC and place it on ∆ PQR in
such a way that AB falls on PQ and BC falls on QR. In this process we shall observe that CA coincides
with RP, i.e., two triangles cover each other exactly. Therefore, ∆ ABC ≅ ∆ PQR.

Since, both the triangles cover each other exactly therefore their corresponding angles are also equal.

Example 4: In the following figures, lengths of the sides of the triangles are indicated. By applying
the SSS congruence criterion, state which pairs of triangles are congruent? In case of
congruent triangles, write the result in symbolic form.

P
A
A
(a) 4 cm 5 cm (b) 3.7 cm 3.7 cm
2 cm 5 cm

D
B C Q R B 2.6 cm 2.6 cm
4 cm 2.5 cm C

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