Grade 9 Mathematics : Chapter: Triangles

Congruence Rules:

SSS (Side–Side–Side) Congruence Rule : Rule : Click Here

The SSS (Side–Side–Side) congruence rule states that if the three sides of one triangle are equal to the three corresponding sides of another triangle, then the two triangles are congruent. This means both triangles have the same shape and size. No angle measurement is required to apply this rule, making it one of the simplest methods to prove congruence. In exam answers, after showing all three pairs of sides are equal, we conclude by writing: ∴ △ABC ≅ △PQR (by SSS rule).

Exam Tip: শেষত লিখিব → ∴ △ABC ≅ △PQR (by SSS rule)

AAS (Angle–Angle–Side) Congruence Rule : Click Here

The AAS (Angle–Angle–Side) congruence rule states that if any two pairs of corresponding angles and one pair of corresponding sides of two triangles are equal, then the triangles are congruent. In this rule, the given side is not included between the two angles. Since the sum of angles in a triangle is fixed, knowing two angles determines the third angle automatically, which helps in proving congruence. In exam answers, after verifying the given conditions, we conclude by writing: ∴ △ABC ≅ △DEF (by AAS rule).

ASA (Angle–Side–Angle) Congruence Rule : Click Here

The ASA (Angle–Side–Angle) congruence rule states that if two angles and the included side of one triangle are equal to the corresponding two angles and the included side of another triangle, then the triangles are congruent. In this rule, the given side must be between the two angles. This condition ensures that both the shape and size of the triangles are exactly the same. In exam answers, after verifying the conditions, we conclude by writing: ∴ △ABC ≅ △DEF (by ASA rule).

SAS (Side–Angle–Side) Congruence Rule :  Click Here

The SAS (Side–Angle–Side) congruence rule states that if two sides and the included angle of one triangle are equal to the corresponding two sides and the included angle of another triangle, then the triangles are congruent. In this rule, the angle must be between the two sides. This condition ensures that both triangles have the same shape and size. In exam answers, after verifying the given conditions, we conclude by writing: ∴ △ABC ≅ △DEF (by SAS rule).

Summary: Valid vs. Invalid Congruence Rules : সমদৃশ্য নিয়ম – সাৰাংশ

1. SAS (Side–Angle–Side) : দুটা বাহু আৰু মাজৰ কোণ সমান → ত্ৰিভুজ সমদৃশ্য


2. ASA (Angle–Side–Angle) : দুটা কোণ আৰু মাজৰ বাহু সমান → ত্ৰিভুজ সমদৃশ্য


3. AAS (Angle–Angle–Side) : দুটা কোণ আৰু কোনো এটা বাহু সমান → ত্ৰিভুজ সমদৃশ্য


4. SSS (Side–Side–Side) : তিনিওটা বাহু সমান → ত্ৰিভুজ সমদৃশ্য


5. RHS (Right–Hypotenuse–Side) : সমকোণী ত্ৰিভুজত অধিকবাহু আৰু এটা বাহু সমান → ত্ৰিভুজ সমদৃশ্য

1. AAA (Angle–Angle–Angle) : মাত্র কোণসমূহ সমান → সমদৃশ্য নহয়, Similarity only


2. SSA (Side–Side–Angle) : দুটা বাহু আৰু কোনো এটা কোণ সমান → Ambiguous case, সমদৃশ্য নোহোৱা পাৰে