FBISE, NCP & NBF-aligned resources for Classes 9–12
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Math Chapter 9 : Topic 1
Similar Polygons
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Two polygons are similar when:
Reasoning: Similarity requires equal angles and proportional sides.
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If two triangles are similar, their corresponding sides are:
Reasoning: Ratios of sides remain constant.
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If scale factor is $2$, area scale factor is:
Reasoning: Area changes by square of scale factor.
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Volume scale factor depends on:
Reasoning: Volume scales cubically.
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Two polygons are NOT similar if:
Reasoning: Angle equality is necessary.
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If side ratio is $3\ :1$, area ratio is:
Reasoning: Square of $3$ is $9$. The surface area of similar solids is proportional to the square of the ratio of their corresponding lengths.
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If volume ratio is $8\ :27$, side ratio is:
Reasoning: Cube root gives $2\ :3$. The volume of similar solids is proportional to the cube of the ratio of their corresponding lengths.
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Similarity is independent of:
Reasoning: Similar shapes may differ in size.
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If two squares are similar, their side ratio equals:
Reasoning: All linear dimensions scale equally.
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Area increases when scale factor increases because:
Reasoning: Area depends on square of dimensions.
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Volume increases faster than area because:
Reasoning: Volume depends on $3D$ dimensions.
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Two polygons with equal angles but unequal sides are:
Reasoning: Similarity requires proportional sides, not equality.
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If scale factor is $1$, figures are:
Reasoning: Same size and shape.
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Perimeter ratio of similar figures equals:
Reasoning: Perimeter scales linearly.
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If side ratio is $1\ :4$, area ratio is:
Reasoning: Square of ratio.
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Similarity is used in:
Reasoning: Maps use scaled similarity.
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If two cubes are similar, volume ratio depends on:
Reasoning: $3D$ scaling.
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If area ratio is $25\ :9$, side ratio is:
Reasoning: Square root gives ratio.
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Similarity preserves:
Reasoning: Shape remains same.
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In similar figures, corresponding angles are:
Reasoning: Angle preservation is key property.
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If scale factor doubles, area becomes:
Reasoning: $2^{2} = 4$
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If scale factor triples, volume becomes:
Reasoning: $3^{3} = 27$
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Similarity ratio is also called:
Reasoning: It scales dimensions.
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Two triangles are similar if:
Reasoning: Angle condition ensures similarity.
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Which property changes in similar figures?
Reasoning: Only size changes, not shape.
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