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Given AGD ||| DHE, the corresponding sides are:

Mathematics

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6.1 Calculate x if △\triangle AGD ∣∣∣||| △\triangle DHE.

  1. Identify corresponding sides from the similarity statement.

    Given △\triangle AGD ∣∣∣||| △\triangle DHE, the corresponding sides are:
    AGDH=GDHE=ADDE\frac{AG}{DH} = \frac{GD}{HE} = \frac{AD}{DE}

  2. Substitute the given lengths from the diagram.

    From the diagram:
    AG=4.5AG = 4.5
    GD=4.8GD = 4.8
    AD=AB+BC+CD=3+x+3.2=6.2+xAD = AB + BC + CD = 3 + x + 3.2 = 6.2 + x
    DH=6.75DH = 6.75
    $HE

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