Bihar Board Class 10 · Maths · Matric exam 2027
Chapter 6: Triangles — notes
The chapter’s 5 parts in the book’s order — the first idea of each and the points Medha Ma’am writes on the board — and the summary at the end. The full lesson and a check question for each part are in the app.
1. Similar Figures
Okay, so you already know about congruent figures.
- • Congruent: same shape AND same size
- • Similar: same shape, size may differ
- • All circles similar; all squares similar
- • All congruent figures are similar (not converse)
- • Polygons similar if: angles equal AND sides proportional
2. Similarity of Triangles and the Basic Proportionality Theorem
Okay, so a triangle is also a polygon.
- • Equiangular triangles: corresponding angles equal
- • Theorem 6.1 (Basic Proportionality/Thales): DE||BC => AD/DB = AE/EC
- • Theorem 6.2 (Converse): AD/DB = AE/EC => DE||BC
- • Example: DE||BC in ABC => AD/AB = AE/AC
3. Criteria for Similarity of Triangles
Okay, so let's talk about when two triangles are similar.
- • Triangle ABC ~ Triangle DEF means angles equal, sides proportional
- • AAA (or AA): equal angles => similar
- • SSS: proportional sides => similar
- • SAS: one equal angle + sides including it proportional => similar
- • Example: AB/RQ = BC/QP = CA/PR => ABC ~ RQP, so angle C = angle P
4. Areas of Similar Triangles
Okay, so — think about this.
- • Theorem 6.6: ar(ABC)/ar(PQR) = (AB/PQ)^2 = (BC/QR)^2 = (CA/RP)^2
- • Example: XY||AC, ar(ABC) = 2 ar(XBY)
- • ABC ~ XBY (AA)
- • AB/XB² = 2/1, so AB/XB = root2
- • AX/AB = (2-root2)/2
5. Pythagoras Theorem through Similarity
Okay, so now let's use similarity to prove something you already know — the Pythagoras Theorem.
- • Theorem 6.7: perpendicular from right angle vertex gives similar triangles
- • Theorem 6.8 (Pythagoras): AC^2 = AB^2 + BC^2
- • Also called Baudhayan Theorem
- • Theorem 6.9 (Converse): square of one side = sum of squares of other two => right angle opposite
- • Example: BC = 2.5m, CA = 6m, AB^2 = (2.5)^2+(6)^2 = 42.25, AB = 6.5m
Summary
Okay, so let's look back at everything we did in this chapter. We started with similar figures — same shape, not necessarily same size. Two polygons are similar only when their corresponding angles are equal, and their corresponding sides are proportional. Both conditions, together. Then we moved to similar triangles. We met the Basic Proportionality Theorem, also called Thales Theorem, and its converse. These connect a line parallel to one side of a triangle with the ratio in which it divides the other two sides. After that came the criteria for similarity — AAA, or just AA, then SSS, then SAS. These let you prove two triangles similar without checking everything. We also saw something nice about areas. For two similar triangles, the ratio of their areas = the square of the ratio of their corresponding sides. And right at the end, using the triangles formed by the perpendicular from the right angle to the hypotenuse, we proved the Pythagoras Theorem — and its converse too. Together they tell us exactly how the sides of a right triangle are related. So, out of all these ideas, which one did you find the most interesting?
AskMedha · Medha Ma’am — Bihar Board Class 10 Maths, Chapter 6. Written from the textbook, checked twice.
Questions parents and students ask
- How do I get the "Triangles" notes as a PDF?
- Press "Save as PDF" — the phone’s print sheet opens; choose "Save as PDF" there. The PDF holds the notes only.
- Where are these notes written from?
- From the chapter’s own textbook text, part by part, in the book’s own terms; a second, independent model then checked every part against the book. The full lesson, a check question for each part and the practice are in the AskMedha app.
The same preparation, with Medha Ma’am — on your phone
Every question of every chapter with its model answer, practice questions in the board’s own shapes, 60 minutes of class a day, written answers marked, a test every Sunday and a WhatsApp report to parents.
Medha Ma’am is an AI teacher, not a live tutor. Every answer is checked twice; a person takes responsibility.