Triangles
Gujarat Board · Class 9 · Mathematics
Quick revision notes for Triangles — Gujarat Board Class 9 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
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Introduction to Triangles and Congruence
- A triangle is a closed figure formed by three intersecting lines with three sides, three angles, and three vertices
- In triangle ABC: sides are AB, BC, CA; angles are ∠A, ∠B, ∠C; vertices are A, B, C
- Congruent figures have the same shape and size - they can cover each other completely
SAS Congruence Rule
- SAS stands for Side-Angle-Side congruence rule
- Two triangles are congruent if two sides and the included angle of one triangle equal the corresponding parts of another
- The angle must be included between the two equal sides
ASA and AAS Congruence Rules
- ASA: Two angles and the included side are equal
- AAS: Two angles and any corresponding side are equal
- If two angles are equal, the third angle is automatically equal (angle sum = 180°)
Properties of Isosceles Triangles
- An isosceles triangle has two equal sides
- Angles opposite to equal sides are equal (Theorem 7.2)
- If two angles of a triangle are equal, the sides opposite to them are equal (Theorem 7.3)
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