Question

In the given figure, division of line segment BC' is shown. Find the ratio of BC and BC' .
Answer Fast Correct answer will be marked as brainliest​

Answer 1

Answer:

3:5

Step-by-step explanation:

From Construction We Can See

Answer 2

Ratio of BC and BC' is  3 : 5

Given:

• Figure showing Details
• B₃C || B₅C'
• BB₁ = B₁B₂ = B₂B₃ = B₃B₄ = B₄B₅

To Find:

• Ratio of BC and BC'

Solution:

• Thales Theorem / BPT ( Basic Proportionality Theorem)  
• if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.
• Properties of angles formed by transversal line  with two parallel lines :
• • Corresponding angles are congruent. ( Equal in Measure)
• • Alternate angles are congruent.  ( Interiors & Exterior  both )  
• • Co-Interior angles are supplementary. ( adds up to 180°)

Step 1:

In ΔBB₃C  and  ΔBB₅C'

∠B = ∠B   ( common)

∠BB₃C  = ∠BB₅C'  ( Corresponding angles)

Hence

ΔBB₃C  ~  ΔBB₅C'  using AA similarity

Step 2:

Corresponding sides of similar triangles are in proportion hence

BC/BC'  = BB₃/BB₅

Step 3:

BB₃  = BB₁ + B₁B₂ + B₂B₃  = 3x   if BB₁ = x

BB₅ = BB₁ + B₁B₂ + B₂B₃ +B₃B₄ + B₄B₅ = 5x

BC/BC'  = 3x/5x

=>  BC/BC'  = 3/5

Hence Ratio of BC and BC' is  3 : 5

( Although Question has not mentioned about details of figure but it should be B₃C || B₅C'  and BB₁ = B₁B₂ = B₂B₃ = B₃B₄ = B₄B₅ )