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Determine apoint which divides a line …

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Determine apoint which divides a line segment of length 12cm internally in the ratio 2:3 also justify your construction

    • Posted by Om Chandani 6 years, 9 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Gaurav Seth 6 years, 9 months ago

    Steps of Construction:

    1. Draw a line segment AB of 12 cm

    2. Through the points A and B draw two parallel line on the opposite side of AB

    3. Cut 2 equal parts on AX and 3 equal parts on BY such that AX1=X1X2 and BX1=Y1Y2=Y2Y3.

    4. Join X2Y3 which intersects AB at P∴APPB=23.

    Justification:

    In ΔAX2P and ΔBY3P, we have

    ∠APX2=∠BPY3 { Because they are vertically opposite angle}

    ∠X2AP=∠Y3BP { Because they are alternate interior angles }

    ΔAX2P ΔBY3P { Because AA similarity }

    ∴ APBP=AX2BY3=23 { Because of C.P.C.T }

    0Thank You

    ANSWER
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