2025 · Basic · Set 5 · Part 2·Q28·3 marks

Triangles

Question

Point E lies on the extended side AD of parallelogram ABCD. BE intersects CD at F. Show that (i) (ii) .

Approach

Use alternate interior angles and AA similarity criterion. (i) In triangles DFE and CFB, corresponding angles are equal (alternate interior and vertically opposite), so by AA, they are similar. (ii) Similarly for triangles AEB and CBF.

Step-by-step working

  1. 1

    Draw correct figure showing parallelogram and extended line

    0.5 marks
  2. 2

    (i) In and , show two pairs of equal angles using alternate interior angles, conclude by AA

    1 mark
  3. 3

    (ii) In and , show two pairs of equal angles, conclude by AA

    1 mark
  4. 4

    Complete reasoning

    0.5 marks

Concepts used

similarityparallelogramtrianglesaa criterion

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