Practice Problems on Basic Proportionality Theorem
1. In triangle ABC, a line DE is drawn parallel to BC and intersects AB at D and AC at E. If AD = 3 cm, DB = 2 cm, and AE = 4.5 cm, find the length of EC.
2. In triangle XYZ, line LM is parallel to YZ, intersecting XY at L and XZ at M. If XL = 5cm, LY = 10 cm, and XM = 8 cm, find the length of MZ.
3. In triangle DEF, line GH is parallel to EF and intersects DE at G and DF at H. If DG = 6 cm, GE = 9 cm, and DH = 8 cm, find the length of HF.
Basic Proportionality Theorem (BPT) Class 10 | Proof and Examples
Basic Proportionality Theorem: Thales theorem is one of the most fundamental theorems in geometry that relates the parts of the length of sides of triangles. The other name of the Thales theorem is the Basic Proportionality Theorem or BPT.
BPT states that if a line is parallel to a side of a triangle that intersects the other sides into two distinct points, then the line divides those sides in proportion.
Let’s learn about the Thales Theorem or Basic Proportionality Theorem in detail, including its statement, proof, and converse as well.
Table of Content
- Basic Proportionality Theorem or Thales Theorem Statement
- Basic Proportionality Theorem Proof
- Construction
- Basic Proportionality Theorem Proof
- Corollary of Thales Theorem
- Articles related to Basic Proportionality Theorem:
- Converse of Basic Proportionality Theorem (BPT)
- Proof
- Construction
- Proof
- Solved Examples on Basic Proportionality Theorem
- Practice Problems on Basic Proportionality Theorem