اے آئی مسودہ — ابھی کسی استاد نے جانچا نہیں۔ اپنے استاد سے تصدیق کریں۔

Mathematics · Class 9 · Chapter 9: Congruent Triangles

8 min

Key points

Two triangles are congruent if they have the same size and shape — all corresponding sides and angles are equal
Four conditions for congruence: SSS, SAS, ASA, and RHS (for right triangles only)
SSS: If three sides of one triangle are equal to three sides of another triangle, then triangles are congruent
SAS: If two sides and included angle of one triangle are equal to corresponding parts of another triangle
ASA: If two angles and included side of one triangle are equal to corresponding parts of another triangle
RHS: If hypotenuse and one side of right triangle are equal to hypotenuse and corresponding side of another right triangle
Corresponding parts of congruent triangles are equal (CPCTC)
Symbol for congruence is ≅, read as 'is congruent to'

Definitions

Congruent Triangles: Two triangles are said to be congruent if they have the same size and shape, i.e., all corresponding sides and angles are equal.
Corresponding Parts: The parts of two congruent triangles which are equal to each other are called corresponding parts.
SSS Condition: If the three sides of one triangle are respectively equal to the three sides of another triangle, then the two triangles are congruent.
SAS Condition: If two sides and the included angle of one triangle are respectively equal to two sides and the included angle of another triangle, then the two triangles are congruent.
ASA Condition: If two angles and the included side of one triangle are respectively equal to two angles and the included side of another triangle, then the two triangles are congruent.

Worked example

In triangles ABC and PQR, AB = PQ = 5 cm, BC = QR = 7 cm, and AC = PR = 6 cm. Prove that triangle ABC ≅ triangle PQR and find the measure of angle B if angle Q = 60°. (6 marks)

△ABC ≅ △PQR by SSS criterion. Since corresponding parts of congruent triangles are equal, ∠B = 60°

Common mistakes

Students confuse similarity with congruency - congruent triangles are equal in size and shape
Writing wrong corresponding vertices when stating congruency - order matters in △ABC ≅ △PQR
Using RHS condition for non-right triangles - it only applies to right triangles
Forgetting to state 'by CPCTC' when finding corresponding parts after proving congruency
Not clearly marking given information and what to prove in geometry proofs

Quick recap

Congruent triangles have equal corresponding sides and angles. Four congruence criteria: SSS (three sides equal), SAS (two sides and included angle), ASA (two angles and included side), RHS (right angle, hypotenuse, and one side). When triangles are congruent, all corresponding parts (CPCT) are equal. Always state which criterion proves congruence.

Generated by AI from Sindh Textbook Board material; review state: ai_unreviewed. MCQs, past-paper references and examiner notes are held back until a teacher has checked them.