Question

In trapezoid ABCD(AB ∥CD), point M∈AD, so that AM:MD=3:5. Line l ∥ AB and passes through point M to intersect diagonal AC and leg BC at points P and N ,respectively. Find AC:PC.
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Answer 1

AC:PC.= 3/5, as  Line l ∥ AB and passes through point M to intersect diagonal AC and leg BC at points P and N.

What is Trapezoid?

A trapezoid, commonly referred to as a trapezium, is a quadrilateral or a polygon with four sides. It has a set of parallel opposing sides and a set of non-parallel sides.

The bases and legs of the trapezoid are known as the parallel and non-parallel sides, respectively.

A trapezoid is a closed, four-sided, two-dimensional figure that has both a perimeter and an area.

The bases of the trapezoid are the two sides of the shape that are parallel to one another. The legs or lateral sides of a trapezoid are the non-parallel sides. The altitude is the shortest distance between two parallel sides.

According to our question-

Consider about the triangles ACB and PCN.

These triangles contain

Since angle C is the common angle and the transversal BC cuts two parallel lines PN and AB, angles ABC and PCN are congruent as equivalent angles by virtue of the reflexive property.

In light of the AA Similarity Theorem, triangles ACB and PCN are comparable.

Similar triangles have matching sides that are proportionate, thus

3/8 / 5/8= 3/5

Hence, Due to the fact that Line l AB and goes via point M to intersect Leg BC and the diagonal AC at points P and N, AC:PC.= 3/5.

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