Tell whether the following statement is true or false:

In the adjoining figure, ABCD is a parallelogram in which E and F are the midpoints of A

B and CD respectively. If G is a line segment that cuts AD, EF and BC at G, P and H

respectively, then GP = PH.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

True

False

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given ABCD is a parallelogram in which E and F are the midpoints of A
B and CD respectively.
abcd is a parallelogram e and f are the midpoints of ab and cd respectively gm is any line intersecting ad ef and bc at g p and h respectively prove t -

abcd is a parallelogram e and f are the midpoints of ab and cd respectively gm is any line intersecting ad ef and bc at g p and h respectively prove t -

As ABCD is a parallelogram, opposite sides are equal in length.
AD = BC AB = DC
Now from the figure,
AB = AE + BE
DC = DF + FC
Therefore, AE = BE = DF = FC.
Since, DF = AE.
AEFD is parallelogram
Similarly, BEFC is parallelogram.
Now, AD || EF || BC. Since, line M is transversal on 3 parallel lines, it divides the line into equal intercept.
Therefore, GP = PH.
Given statement is true.
Hence, option 1 is correct.

Watch 3-min video & get full concept clarity