Q1. In triangle ABC, if DE is parallel to BC, which ratio is correct?
✔ BPT states the segments on the sides are proportional, not part to whole.
Q2. If AD=3, DB=6, and AE=4, what is EC?
✔ Cross multiply 3x = 24 to find the missing segment length.
Q3. What is the essential condition for BPT?
✔ The theorem only applies when a line cuts two sides parallel to the third.
Show transcript
[Slide 1] Understanding BPT Intuition
Imagine a triangle with a line cutting through it parallel to the base. This line splits the other two sides into matching ratios. It is like slicing a pizza evenly from the top down.
[Slide 2] The BPT Formula
If DE is parallel to BC, the ratio of AD to DB equals AE to EC. Remember, you compare the top segment to the bottom segment on each side.
[Slide 3] Worked Example Setup
Consider a triangle where DE runs parallel to the base BC. We know three lengths and need to find the fourth segment EC.
[Slide 4] Solving the Example
Plug in the numbers to get two over four equals three over x. Cross multiplying gives us two x equals twelve, so x is six.
[Slide 5] Common Mistake Alert
Students often mistake the ratio by comparing a segment to the whole side. BPT requires comparing the two smaller segments on each side only.
[Slide 6] Quick Recap
Always verify the lines are parallel before applying the theorem. Keep your ratios consistent between the two sides of the triangle.