1. Fill in the blanks
(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.
2. Examples (two each)
(i) Similar figures — two examples
Example A — Two rectangles with same shape (different sizes)
Diagram (ASCII):
Reason: All angles = 90° and corresponding sides are in same ratio (scale factor). ⇒ Similar.
Example B — Two equilateral triangles
Reason: All corresponding angles equal (60°) ⇒ Similar.
(ii) Non-similar figures — two examples
Example C — Square and rectangle with different aspect ratio
Reason: Angles equal but side ratios differ (not proportional) ⇒ Not similar.
Example D — Rhombus and square
3. State whether the following quadrilaterals are similar or not (how to decide + examples)
Note: I couldn’t extract the image of Fig. 6.8 exactly from the PDF preview here. Below I give the correct test you should apply to each pair in Fig. 6.8 and show three typical example-pairs (with answers). If you want, paste or upload the Fig.6.8 image and I’ll mark each one directly.
How to decide (step-by-step):
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Compare corresponding angles. If all four corresponding angles of one quadrilateral equal those of the other, proceed; otherwise they are not similar.
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Compare corresponding side ratios. Compute the ratios of corresponding sides (order the vertices consistently). If all ratios are equal (same scale factor), they are similar.
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If only one of the two tests holds (angles equal but not proportional sides, or sides proportional but angles different) → not similar. These rules follow the textbook definition.
Typical example pairs (illustrative, with answers):
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Pair 1 — Similar (scaled copy)
Angles equal; corresponding side ratios equal ⇒ Similar.
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Pair 2 — Not similar (angles same but side ratios differ)
Angles all 90°, but side ratios not equal ⇒ Not similar.
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Pair 3 — Not similar (sides proportional by chance but angles differ)
Even if some side-length ratios match, angles differ ⇒ Not similar.