Tell whether the following statement is true or false:

In the adjoining figure, ABCD is a quadrilateral. A line through D, parallel to AC, meets BC produced in P. Then area of triangle ABP = area of quadrilateral ABCD.

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True

False

answer is A.

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Detailed Solution

Given a quadrilateral ABCD.
In the adjoining figure, ABCD is a quadrilateral. A line through D, parallel to AC, meets BC produced in P. Prove that ar (△ ABP) = ar (quad. ABCD). - Sarthaks eConnect |

In the adjoining figure, ABCD is a quadrilateral. A line through D, parallel to AC, meets BC produced in P. Prove that ar (△ ABP) = ar (quad. ABCD). - Sarthaks eConnect |

As, triangles ACP and ACD lies between same parallel and same base.
Area of triangle ACP = Area of triangle ACD
Now, adding area of triangle ABC on both side.
Area of triangle ACP + Area of triangle ABC = Area of triangle ACD + Area of triangle ABC
Area of triangle ABP = Area of quadrilateral ABCD
Given statement is true.
Hence, option 1 is correct.

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