Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
526 views
in Quadrilaterals by (26.9k points)
closed by

ABC is a triangle. D is a point on AB such that AD = \(\frac{1}{4}\)AB and E is a point on AC such that AE = AC. 

Prove that DE = \(\frac{1}{4}\)BC.

1 Answer

+1 vote
by (27.3k points)
selected by
 
Best answer

Given, 

Let P and Q be the mid points of AB and AC respectively

Then, 

PQ || BC and 

PQ = \(\frac{1}{2}\) BC ....(i)

In ∆APQ, 

D and E are mid points of AP and AQ resp.

∴ DE || PQ , 

DE = \(\frac{1}{2}\)PQ ...(ii)

From (i) and (ii),

DE = \(\frac{1}{2}\)PQ = \(\frac{1}{2}\)(\(\frac{1}{2}\) BC)

DE = \(\frac{1}{4}\) BC Proved.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...