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

Similar Reads

Basic Proportionality Theorem or Thales Theorem Statement

Thales’s Theorem or Basic Proportionality Theorem (BPT) states that if a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio....

Basic Proportionality Theorem Proof

Let’s prove the Basic Proportionality Theorem....

Converse of Basic Proportionality Theorem (BPT)

The Converse of the Basic Proportionality Theorem (BPT) or Thales’s Theorem states that if a line intersects two sides of a triangle and divides the sides proportionally, then the line is parallel to the third side of the triangle....

Solved Examples on Basic Proportionality Theorem

Let’s solve some questions on the Basic Proportionality Theorem....

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....

Summary – Basic Proportionality Theorem

The Basic Proportionality Theorem, also known as Thales’ Theorem, states that if a line is drawn parallel to one side of a triangle, intersecting the other two sides, it divides those sides proportionally. In simpler terms, this means that the segments created on each side of the triangle are proportional to each other. For example, if a line parallel to one side of a triangle intersects the other two sides, then the ratios of the lengths of the segments on those sides will be equal. This theorem is fundamental in geometry as it provides a method to solve various problems related to proportional relationships within triangles....

FAQs on Basic Proportionality Theorem

What is Basic Proportionality Theorem?...