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Question

In the figure, angle A equals angle C E D, AB = 9 cm, AD = 7 cm, CD = 8 cm and CE = 10 cm Then DE = ?

  1. 4 cm    
  2. 6 cm    
  3. 8 cm    
  4. 10 cm    

hintHint:

find the similar triangles and apply the side ratio property

The correct answer is: 6 cm


    6 CM
    Triangles ABC and CDE  are similar by the angle angle axiom. , angle C being the common angle.
    CE/AC = CD / CB = DE/ AB
    AC = AD + CD = 7 + 8 = 15 cm
    10/15 = DE/ 9
    DE = 6 cm.

    if 2 angles are same in a triangle, then the triangles are similar. we can use the property that ratio of sides remains same in similar triangles.

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