Basic Proportionality Theorem Concepts

The video tutorial explains the Basic Proportionality Theorem, also known as Thales' Theorem. It begins with the theorem's statement and proceeds to construct a geometric setup involving a triangle and a line parallel to one of its sides. The tutorial then calculates the areas of various triangles formed in the setup, leading to the derivation of key equations. These equations are used to prove that the segments of the triangle's sides are divided proportionally, thus proving the theorem.

What is another name for the Basic Proportionality Theorem?

• Pythagorean Theorem

• Thales' Theorem

• Euclid's Theorem

• Archimedes' Principle

In triangle ABC, if line DE is parallel to BC, which sides does it intersect?

• AB and AC

• BC and AC

• AB and BC

• AC and DE

What is the purpose of drawing perpendiculars DM and EN in the construction?

• To find the midpoint of the triangle

• To calculate the area of the triangles

• To determine the length of DE

• To prove the triangle is isosceles

How is the area of a triangle generally calculated?

• Product of all angles

• Sum of all sides

• Base times height

• Half the product of base and height

Which concept is used to prove the theorem in the video?

• Area of a triangle

• Congruence of triangles

• Pythagorean Theorem

• Similarity of triangles

What is the relationship between the areas of triangles BDE and DEC?

• BDE is twice DEC

• BDE is half of DEC

• BDE is equal to DEC

• BDE is unrelated to DEC

What does the Basic Proportionality Theorem help to prove in triangle ABC?

• AD = AE

• AD/DB = AE/EC

• AB = AC

• BC = DE

What is the significance of the line DE being parallel to BC?

• It makes the triangle right-angled

• It divides the triangle into two equal areas

• It ensures the sides are divided proportionally

• It makes the triangle isosceles

What is the result of the equation AD/DB = AE/EC?

• The triangle is congruent

• The angles are equal

• The sides are proportional

• The triangle is equilateral

Which triangles are compared to establish the proportionality in the proof?

• ADE and DEC

• BDE and DEC

• ADE and ABC

• ABC and BDE