Mathematics
Grade9
Easy

Question

If AD is the bisector of angle A. find the fraction numerator A C over denominator A B end fraction.

  1. 3 over 5
  2. 5 over 3
  3. 2 over 5
  4. 1 fifth

hintHint:

If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.

The correct answer is: 3 over 5



    In, triangleADB and triangleADC
    angleDAB = angleDAC (AD is the bisector ofangle A )
    angleADB = angleADC
    Thus, by AA similarity criterion  triangleADB tilde triangleADC
    fraction numerator A C over denominator A B end fraction space equals space fraction numerator C D over denominator D B end fraction space equals space fraction numerator 1.5 over denominator 2.5 end fraction space equals space 3 over 5 space left parenthesis space c o r r e s p o n d i n g space s i d e space o f space s i m i l a r space t r i a n g l e s right parenthesis

    Thus, fraction numerator A C over denominator A B end fraction = 3 over 5.

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