Seshu cheera

✍️ Chapter 11: Constructions – Class 10 Maths 🔍 Concepts Covered This chapter focuses on geometrical constructions using a compass and straightedge only , without measuring instruments like protractors. Two major types of constructions are covered: 🧠 1. Division of a Line Segment in a Given Ratio (m:n) ➤ Concept : Divide a given line segment internally in the ratio m : n m:n using only ruler and compass. 📌 Construction Steps : Let’s divide a line segment A B AB in the ratio m : n m:n : Draw A B AB using a scale. Draw a ray A X AX making an acute angle with A B AB . Mark m + n m+n equal divisions on A X AX using compass — say A 1 , A 2 , . . . , A m + n A_1, A_2, ..., A_{m+n} . Join A m + n A_{m+n} to B B . Draw a line through A m A_m parallel to A m + n B A_{m+n}B (using construction of a triangle with equal corresponding angles). This line meets A B AB at point P P . ✅ Hence, P P divides A B AB in the ratio m : n m:n . 🧠 2. Construction...

  Class 10 CBSE Maths – Chapter 6:Triangles 🔹 Key Concepts and Theorems ✅ Similar Figures Figures having the same shape but not necessarily the same size. All congruent figures are similar but not all similar figures are congruent. ✅ Similar Triangles Two triangles are similar if: Their corresponding angles are equal Their corresponding sides are in the same ratio (proportional) Criteria for Similarity of Triangles: AA (Angle-Angle) Criterion : Two triangles are similar if two angles of one triangle are respectively equal to two angles of another triangle. SSS (Side-Side-Side) Criterion : If the sides of two triangles are in the same ratio, then the triangles are similar. SAS (Side-Angle-Side) Criterion : If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are in the same ratio. ✅ Basic Proportionality Theorem (Thales Theorem) Statement: If a line is drawn parallel to one side of a triang...