Page 197 - ICSE Math 7

B

2. In the adjoining figure, AD = CF and CB = DE. Prove that
(a) AB is parallel to EF. A D C F
(b) AB = EF.

A E

3. In the adjoining figure, ∆ ABC is isosceles.
Also, ∠PBC = ∠PCB. Prove that

(a) ∆ APB ≅ ∆ APC.
P
(b) ∠APB = ∠APC.
B C

T C
4. In the parallelogram FACT, show that
(a) ∆ FAT ≅ ∆ CTA.
(b) ∠ = ∠TAC.

F A
A
5. ∆ ABC is isosceles in which AB = AC and AD is one of its altitudes.

(a) State any three pairs of equal parts in ∆ ADB and ∆ ADC.
(b) Is ∆ ADB ≅ ∆ ADC? If yes, mention the criteria used.
(c) Is BD = CD? Why or why not?
(d) Is ∠BAD = ∠CAD? Why or why not?

B D C
6. Raman goes to buy two triangular pieces of glass. He wants the glasses to be identical in shape
and size. Which of the given triangular glasses should he buy?

(a) 6 cm (b) 6 cm (c) (d)
10 cm 5 cm 6 cm
8 cm
5 cm 9 cm 7 cm 5 cm 7 cm
6 cm
Explain your answer using the criterion for congruency of triangles.

THINK SMART

1. Draw two triangles of equal areas on a squared sheet such that:
(a) the triangles are congruent. (b) the triangles are not congruent.
What can you say about the perimeters of these triangles?

2. Can you draw two triangles such that they have five pairs of congruent parts but the triangles are
not congruent?

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