Similarity
ICSE · Class 10 · Mathematics
Flashcards for Similarity — ICSE Class 10 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Get startedWhat are similar figures? How do they differ from congruent figures?
Answer
Similar figures have the same shape but may have different sizes. Their corresponding angles are equal and corresponding sides are proportional. Congruent figures have both same shape and same size, w…
State the definition of similar triangles with mathematical notation.
Answer
Two triangles ABC and PQR are similar (△ABC ~ △PQR) if: (i) Their corresponding sides are proportional: AB/PQ = BC/QR = AC/PR (ii) Their corresponding angles are equal: ∠A = ∠P, ∠B = ∠Q, ∠C = ∠R…
What is the AA (Angle-Angle) similarity criterion?
Answer
If two angles of one triangle are equal to the corresponding two angles of another triangle, then the two triangles are similar. This is also called AA similarity criterion. Since the sum of angles in…
Explain the SAS (Side-Angle-Side) similarity criterion.
Answer
If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, then the two triangles are similar. For triangles ABC and PQR: if ∠A = ∠P an…
State the SSS (Side-Side-Side) similarity criterion.
Answer
If the three sides of one triangle are proportional to the three sides of another triangle, then the two triangles are similar. For triangles ABC and PQR: if AB/PQ = BC/QR = AC/PR, then △ABC ~ △PQR.
State the Basic Proportionality Theorem (Thales' Theorem).
Answer
If a line is drawn parallel to one side of a triangle, intersecting the other two sides, then it divides the other two sides proportionally. In triangle ABC, if DE || BC, then AD/DB = AE/EC.
State the converse of the Basic Proportionality Theorem.
Answer
If a straight line divides any two sides of a triangle proportionally, then the line is parallel to the third side. In triangle ABC, if AD/DB = AE/EC, then DE || BC.
What does the symbol '~' represent in geometry?
Answer
The symbol '~' represents 'is similar to'. For example, △ABC ~ △PQR means triangle ABC is similar to triangle PQR.
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