CBSE · Class 6-12

Class 10 · Mathematics (Basic)

Unit 6 · Class 10Mathematics (Basic)

Triangles

Similar triangles, criteria for similarity (AAA, SAS, SSS), Basic Proportionality Theorem (Thales) and Pythagoras theorem.

Lessons

6 concepts

1
Similar Figures
Two figures are similar if they have the same shape (but not necessarily the same size). For triangles, this means all pairs of corresponding angles are equal and all pairs of corresponding sides are proportional. The co…
2
Basic Proportionality Theorem (Thales)
If a line is drawn parallel to one side of a triangle and intersects the other two sides in distinct points, then it divides those two sides in the same ratio: in $\triangle ABC$ with $DE\parallel BC$ , $AD/DB = AE/EC$ .
3
Similarity Criteria
AAA (angle-angle-angle): if two triangles have their three pairs of angles equal, they are similar. AA is sufficient. SSS (side-side-side ratio): three pairs of corresponding sides in the same ratio. SAS (side-angle-side…
4
Areas of Similar Triangles
If two triangles are similar with sides in ratio $k$ , their areas are in ratio $k^2$ . Formally, $\dfrac{\text{ar}(\triangle ABC)}{\text{ar}(\triangle DEF)} = \left(\dfrac{AB}{DE}\right)^2 = \left(\dfrac{BC}{EF}\right)^2 …
5
Pythagoras Theorem and Converse
In a right triangle with legs $a, b$ and hypotenuse $c$ : $c^2 = a^2 + b^2$ . Converse: if in a triangle with sides $a, b, c$ we have $c^2 = a^2 + b^2$ , then the angle opposite $c$ is a right angle. Pythagorean triples: $(…
6
Applications
Similarity + Pythagoras are heavily used in coordinate geometry (distance/section formulas), trigonometry (defining ratios), heights & distances, and geometric constructions. Look for shared angles (common angle at a ver…

Skills to practise

Skill · medium

Triangles — Practice