Question

In the given figure, if AB/DC, then AP is equal to​

Answer 1

Answer:

Step-by-step explanation:

garina 1524 and we get the answer as 102

Answer 2

Given: In a trapezium, AB || DC, AC = BD = 7.5 cm

To find: AP is equal to

Solution:

In Triangle APD and Triangle BPC,

L APD = L BPC ( vertically opposite angles are equal )

L DAP = L PCB ( alternate interior angles with AC as transversal )

L ADP = L PCB ( alternate interior angles with BD as transversal )

Since all the angles of the triangle ΔAPD are equal to the corresponding angles of the triangle, ΔBPC

ΔAPD and ΔBPC are similar to each other by AAA similarity criteria.

Thus we can say that,

AP / BP = PD / PC __(1)

Now,

AC = AP + PC   => PC = AC -- AP   __(2)

BD = BP + PD   => PD = BD -- BP   __(3)

Putting 2 and 3 in 1,

AP / BP = (BD -- BP) / (AC -- AP)

AP / BP = 7.5 - BP / 7.5 - AP

Comparing Numerator and Denominator,

AP = BP