Practice - Basic Proportionality Theorem (Thales’ Theorem)
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Practice Questions
Test your understanding with targeted questions
If line DE is parallel to side BC in triangle ABC, and AD = 2 cm, DB = 3 cm, find AE if EC = 4 cm.
💡 Hint: Set up the proportion and solve for AE.
In triangle XYZ, if XY = 5 cm and YZ = 12 cm, and line AB is drawn parallel to YZ, divides XZ into segments 3 cm and 9 cm. Confirm if these segments are proportional.
💡 Hint: Reduce the fractions to see if they are equal.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the Basic Proportionality Theorem state?
💡 Hint: Think about how dividing sides in similar triangles relates.
True or False: The segments created from the parallel line must be equal.
💡 Hint: Think about ratios rather than equality.
1 more question available
Challenge Problems
Push your limits with advanced challenges
You have triangle ABC with angles 40°, 60°, and 80°. A line DE is drawn parallel to side BC, dividing AB and AC at points D and E. Prove that the segments are proportional.
💡 Hint: Remember the properties of similar triangles.
Given a triangle with sides 'a', 'b', and 'c', and a parallel line divides it into segments of length 4, and 6 cm, calculate the lengths of all sides if maintained in proportion.
💡 Hint: Establish known values and ratios among segments.
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