Triangles

Triangles

1. 1. Introduction to Triangles

   • 1.Basics of Triangles
     • • Concept of triangle • Identifying Triangles • Elements of Triangles (vertex, interior angles, exterior angles) • Regions of Triangles
   • 2.Classification of Triangles
     • • Classification based on sides • Classification based on angles

2. 2. Properties and Theorems of Triangles

   • 1.Angle Sum Property
     • • Angle Sum Property - Theorems / Proofs / Applications
   • 2.Exterior Angle Property
     • • Exterior Angle Property - Theorems / Proofs / Applications
   • 4.Properties of Isosceles triangle
     • • Base angle Property of isosceles triangle
   • 3.Properties of Right angled triangle
     • • Pythagoras Theorem and its Converse - Theorems / Proofs / Applications • Pythagorean Triplet
   • 5.Property of Inequality
     • • Properties of Inequality in Triangles
   • 6. Midpoint Theorem
     • • Midpoint Theorem- Proof and Applications

3. 3.Special Lines and Circles in Triangles

   • 1.Concurrent Lines in a Triangle:
     • • Definition of Median, Altitude, Angle bisector, Perpendicular bisector, Centroid and Orthocenter etc • Characteristics with respect to different types of triangles
   • 2.Circles in Triangles
     • • Definition of Circumcirlce, Circumcentre, Incircle, Incentre • Characteristics with respect to different types of triangles

4. 4. Congruence of Triangles

   • 1.Basics of Congruence
     • • Concept of congruence • Congruency of triangles • Meaning of corresponding sides and corresponding angles • Representation of congruent triangles • CPCTC
   • 2. Rules of Congruence
     • • SSS Congruency- Theorem / Proof / Applications • SAS Congruency - Theorem / Proof / Applications • ASA Congruency - Theorem / Proof / Applications • RHS Congruency - Theorem / Proof / Applications

5. 5. Similarity in Triangles

   • 1. Concept of Similar Triangles
     • • Basics of Similarity • Concept of Similar Triangles • Representation of Similar Triangles
   • 2.Rules and Theorems for Similarity of Triangles
     • • Criteria for similarity of two triangles:SAS-similarity • AA / AAA-similarity • SSS-similarity • Right Triangle - Similarity Theorem • Angle - Bisector Theorem its Converse and other theorems.

6. 6. Construction and Measurement of triangles

   • 1. Construction and Measurement of triangles
     • • Construction of an Triangle(all types) • Construction of Circumcircle of a Triangle • Construction of Incircle of a Triangle • Measure the sides of the given triangle • Measure the angles of the given triangle