Curriculum

Course: Mathematics — Second Preparatory

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Curriculum

Mathematics — Second Preparatory

Unit 1: Real Numbers

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Unit 2: Algebra

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Unit 3: Geometry

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Unit 4: Statistics

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Text lesson

Congruence

Mathematics — Second Preparatory

Congruence

Worked examples

Worked examples

Comparison aspect	Main idea	Keywords
Example 1	Triangles ABC and DEF have AB = 3 cm BC = 4 cm AC = 5 cm and DE = 3 cm EF = 4 cm DF = 5 cm. Are they congruent?	Trianglescongruent
Solution	All corresponding sides are equal, so the triangles are congruent by SSS. Each has perimeter 12 cm, and each has area 6 cm², because it is a right triangle with legs 3 and 4.	correspondingsidesequaltriangles
Example 2	In triangles ABC and DEF AB = DE = 5 cm angle B = angle E = 60° and BC = EF = 7 cm. Explain why they are congruent	trianglesangleExplaincongruent
Solution	Two sides and the included angle are equal in both triangles which is the SAS case. So the triangles are congruent AC = DF and angle A = angle D	sidesincludedangleequal
Example 3	Triangles ABC and PQR are congruent with AB = 8 cm BC = 5 cm AC = 7 cm. Also PQ = x + 1 cm QR = 5 cm and PR = 7 cm. Find x	TrianglescongruentFind

Comparison aspect	Main idea	Keywords
Solution	The side corresponding to AB is PQ so PQ = AB = 8. That gives x + 1 = 8 so x = 7. Check: the three sides 8 5 and 7 are equal in both triangles	sidecorrespondinggivesCheck
Example 4	In triangles ABC and DEF angle A = angle D = 50° angle B = angle E = 70° and AB = DE. Find angle C	trianglesangleFind
Solution	The angles of a triangle add up to 180° so angle C = 180° − 50° − 70° = 60°. The triangles are congruent by ASA so angle F = angle C = 60°	anglestriangleangletriangles

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