Triangles Notes

✓ Free notes Class 10 Math 1 study file

About these notes

Class 10 Math Triangles notes give clear steps for proving similarity, using the Basic Proportionality Theorem and converting side ratios to area ratios (useful for numeric length problems). Main sub-topics: AA, SAS and SSS similarity tests; Basic Proportionality Theorem (DE ∥ BC ⇒ AD/DB = AE/EC) and its converse; area ratio = (corresponding side ratio)²; matching corresponding vertices; applications to heights and segment calculations. For Class 10 CBSE and Bihar Board students preparing for board exams, school chapter tests and mock tests — Merit Spring ROH also offers site-wide chapter tests and mock tests.

Key points you will learn

Class 10 Math Triangles — similarity tests, BPT and area-ratio methods
AA criterion: two equal angles ⇒ triangles are similar
SAS and SSS similarity: sides proportional with included angle equal, or three sides proportional
Basic Proportionality Theorem (Thales): DE ∥ BC ⇒ AD/DB = AE/EC and converse
Area ratio of similar triangles = (corresponding side ratio)², e.g. (a/b)²
Always match corresponding vertices before writing proportions; order matters
Use cross-multiplication to solve for unknown segments and check units
Similarity applications: find heights, distances, divided segments and scale problems

What is inside this chapter

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Triangles

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Questions students ask

What is similarity of triangles?

Two triangles are similar if their corresponding angles are equal and their corresponding sides are proportional. Common tests used are AA, SAS (sides in proportion with included angle equal) and SSS (three sides proportional).

How to prove two triangles are similar in Class 10 problems?

Start by identifying matching vertices and then use AA, SAS or SSS: show two equal angles (AA) or show sides in proportion with included angle equal (SAS), or three sides proportional (SSS), then write corresponding proportions.

If the ratio of corresponding sides is 3:5, what is the ratio of their areas?

The area ratio is 9:25 because area ratio = (side ratio)², so (3/5)² = 9/25. Square the linear ratio to convert to area ratio.

In triangle ABC, DE ∥ BC, AD = 4 cm, DB = 6 cm and AE = 6 cm. Find EC.

Use AD/DB = AE/EC ⇒ 4/6 = 6/EC, so EC = (6×6)/4 = 9 cm. Write the proportion, cross-multiply, and simplify.

Where can I find Class 10 Math Triangles notes, important questions and MCQ?

Open the Triangles page on Merit Spring ROH for the chapter notes; for important questions and MCQ use the site-wide chapter tests and mock tests provided on Merit Spring ROH to practice exam-style questions.

More Math chapters

Real Numbers Polynomials Pair of Linear Equations in Two Variables Quadratic Equations Arithmetic Progressions Coordinate Geometry All chapters →

Class 10 — other subjects

Science Social Science Computer ENGLISH HINDI SANSKRIT

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