Q1
What defines similar triangles?
AEqual angles and proportional sides
BEqual sides only
CEqual angles only, without proportional sides
DNo specific relationship
ICSEClass 10 (ICSE)MathematicsCh 15 · Topic 1
Similarity
Similar triangles have the same shape but different sizes, with corresponding angles equal and corresponding sides in proportion.
Core concept
Two triangles are similar if their corresponding angles are equal (AA similarity) or if their corresponding sides are in proportion (SSS similarity).
How it works
The Basic Proportionality Theorem (Thales' theorem) states that a line parallel to one side of a triangle divides the other two sides proportionally.
Why it matters
Similar triangles have equal ratios of corresponding sides, and the ratio of their areas equals the square of the ratio of corresponding sides.
Key detail
Understanding similarity helps solve problems involving scale models, indirect measurement, and proving geometric relationships.
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• Similar triangles have equal corresponding angles.
• Their corresponding sides are proportional.
• AA similarity: equal corresponding angles.
• SSS similarity: proportional corresponding sides.
• Basic Proportionality Theorem (Thales'): parallel line divides sides proportionally.
• Area ratio = square of side ratio.
• Similarity helps with scale models.
• It also helps with indirect measurement.