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If a point C lies between two points A and B such that AC = BC, then prove that AC = ½ AB. Explain by drawing the figure.Q.4

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Find this important question of ncert class 9th of chapter Introduction To Euclid’s Geometry.Sir please help me to find out the easiest and simplest solution of question 4 of exercise 5.1, give me the best solution of this question.If a point C lies between two points A and B such that AC = BC, then prove that AC = ½ AB. Explain by drawing the figure.

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  1. Solution:

    Ncert solutions class 9 chapter 5-2

    Given that, AC = BC

    Now, adding AC both sides.

    L.H.S+AC = R.H.S+AC

    AC+AC = BC+AC

    2AC = BC+AC

    We know that, BC+AC = AB (as it coincides with line segment AB)

    ∴ 2 AC = AB (If equals are added to equals, the wholes are equal.)

    ⇒ AC = (½)AB.

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