Practice Basic Proportionality Theorem (thales’ Theorem) (1.6) - Theorems in Geometry & Trigonometry

Practice: Basic Proportionality Theorem (Thales’ Theorem)

Lesson 1.6Theorems in Geometry & Trigonometry

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9 questions

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Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
If line DE is parallel to side BC in triangle ABC, and AD = 2 cm, DB = 3 cm, find AE if EC = 4 cm.
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Set up the proportion and solve for AE.
Question 2.
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.
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Reduce the fractions to see if they are equal.
3Question 3.
What does the Basic Proportionality Theorem state?
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Think about how dividing sides in similar triangles relates.
4Question 4.
True or False: The segments created from the parallel line must be equal.
- True
- False
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Think about ratios rather than equality.
Question 5.
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.
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Remember the properties of similar triangles.
Question 6.
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.
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Establish known values and ratios among segments.

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