Similarity, Area & Proportions
A structured problem set for ICSE / CBSE board practice
📚 Quick Recap – Geometry Essentials
1. Similarity of Triangles
Two triangles are similar if their corresponding angles are equal and corresponding sides are proportional. The main criteria are:
- AA (Angle‑Angle): Two angles of one triangle equal to two angles of another.
- SAS (Side‑Angle‑Side): One angle equal and the sides including it are proportional.
- SSS (Side‑Side‑Side): All three sides are proportional.
2. Basic Proportionality Theorem (Thales)
If a line is drawn parallel to one side of a triangle intersecting the other two sides, it divides those sides in the same ratio.
3. Mid‑Point Theorem
The line segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length.
4. Properties of Parallelograms
- Opposite sides are equal and parallel.
- Diagonals bisect each other.
- Opposite angles are equal.
5. Area Ratios of Similar Triangles
The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
💡 Pro‑tip: Always look for parallel lines – they are the key to setting up similarity and proportional segments.
No comments:
Post a Comment