1Fill in the blanks using the correct word given in brackets:
Answer:
(i) All circles are similar.
(ii) All squares are similar.
(iii) All equilateral triangles are similar.
(iv) Two polygons of the same number of sides are similar, if (a) their corresponding angles are equal and (b) their corresponding sides are proportional. Reference: Section 6.2, Page 122–123
2Give two different examples of pair of (i) similar figures. (ii) non-similar figures.
Answer:
(i) Similar figures: Two equilateral triangles of side 3 cm and 5 cm; two circles of radius 2 cm and 7 cm.
(ii) Non-similar figures: A square and a rectangle; a circle and a triangle. Reference: Section 6.2, Fig. 6.6 and 6.7, Page 124
3State whether the following quadrilaterals are similar or not (Fig. 6.8).
Answer:
The quadrilaterals are not similar. Although corresponding angles are equal (all 90°), the sides are not in proportion: 3/1.5 = 2, but 3/3 = 1 → ratios differ. Reference: Section 6.2, Fig. 6.8, Page 125
1In Fig. 6.17, DE || BC. Find EC in (i) and AD in (ii).
Answer:
(i) By Basic Proportionality Theorem (Theorem 6.1):
AD/DB = AE/EC → 1.5/3 = 1/EC → EC = 2 cm.
(ii) AD/7.2 = 1.8/5.4 → AD = (1.8 × 7.2)/5.4 = 2.4 cm. Reference: Theorem 6.1, Page 126–127
2E and F are points on sides PQ and PR of △PQR. For each case, state whether EF || QR.
Answer:
Use converse of Basic Proportionality Theorem (Theorem 6.2):
(i) PE/EQ = 3.9/3 = 1.3; PF/FR = 3.6/2.4 = 1.5 → Not parallel.
(ii) PE/EQ = 4/4.5 = 8/9; PF/FR = 8/9 → EF || QR.
(iii) PE/PQ = 0.18/1.28 = 9/64; PF/PR = 0.36/2.56 = 9/64 → EF || QR. Reference: Theorem 6.2, Page 128
3In Fig. 6.18, if LM || CB and LN || CD, prove that AM/AB = AN/AD.
Answer:
In △ABC, LM || CB ⇒ AM/AB = AL/AC (Theorem 6.1).
In △ADC, LN || CD ⇒ AN/AD = AL/AC.
∴ AM/AB = AN/AD. Reference: Example 2 logic, Page 129
15A vertical pole of length 6 m casts a shadow 4 m long. At the same time, a tower casts a shadow 28 m long. Find the height of the tower.
Answer:
Let height of tower be h.
Since sun rays are parallel, triangles are similar (AA criterion).
So, 6/4 = h/28 → h = (6 × 28)/4 = 42 m. Reference: Example 7 logic, Page 141
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