State, true or false: The diagonals of a trapezium divide each other into proportional segments. - Mathematics

State, true or false:

The diagonals of a trapezium divide each other into proportional segments.

MCQ

True or False

This statement is True.

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Areas of Similar Triangles Are Proportional to the Squares on Corresponding Sides

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Chapter 15 Similarity (With Applications to Maps and Models)
Exercise 15 (A) | Q 11.7 | Page 213

In quadrilateral ABCD, diagonals AC and BD intersect at point E such that
AE : EC = BE : ED. Show that: ABCD is a trapezium.

In a trapezium ABCD, side AB is parallel to side DC; and the diagonals AC and BD intersect each other at point P. Prove that :

P is a point on side BC of a parallelogram ABCD. If DP produced meets AB produced at point L, prove that: DP : PL = DC : BL.

In the given figure, AD = AE and AD² = BD × EC. Prove that: triangles ABD and CAE are similar.

In the given figure, DE || BC, AE = 15 cm, EC = 9 cm, NC = 6 cm and BN = 24 cm. Find lengths of ME and DM.

In the given figure, DE || BC, AE = 15 cm, EC = 9 cm, NC = 6 cm and BN = 24 cm.

In ΔABC, angle ABC is equal to twice the angle ACB, and bisector of angle ABC meets the opposite side at point P. Show that: AB × BC = BP × CA

Triangle ABC is similar to triangle PQR. If AD and PM are corresponding medians of the two triangles, prove that : `("AB")/("PQ") = ("AD")/("PM")`.

Triangles ABC and DEF are similar.
If area (ΔABC) = 36 cm², area (ΔDEF) = 64 cm² and DE = 6.2 cm, find AB.