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
2.0k views
in Triangles by (56.3k points)

In figure, the sides BA and CA have been produced such that BA = AD and CA = AE. Prove that segment DE ∥ BC.

1 Answer

+1 vote
by (30.5k points)
selected by
 
Best answer

Sides BA and CA have been produced such that BA = AD and CA = AE. 

To prove: DE ∥ BC

Consider △BAC and △DAE, 

BA = AD and CA= AE (Given) 

∠BAC = ∠DAE (vertically opposite angles)

By SAS congruence criterion, we have 

△BAC ≃ △DAE 

We know, corresponding parts of congruent triangles are equal 

So, BC = DE and ∠DEA = ∠BCA, ∠EDA = ∠CBA 

Now, DE and BC are two lines intersected by a transversal DB s.t. 

∠DEA=∠BCA (alternate angles are equal) 

Therefore, DE ∥ 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

...