Sarthaks Test
0 votes
714 views
in Mathematics by (7.9k points)

Prove that the medians of an equilateral triangle are equal.

1 Answer

0 votes
by (13.1k points)
selected by
 
Best answer

Given to prove that the medians of an equilateral triangle are equal

Median: The line joining the vertex and midpoint of opposite side.

Now, consider an equilateral triangle ABC

Let D,E,F are midpoints of , BC CA and AB

Then,  AD, BE and CF are medians of ΔABC

Now,

Since ΔABC is an equilateral triangle

ABD = BCE     [From (3)]

[ABD and ABC and BCE and BCA  are same]

So, from SAS congruence criterion, we have

[Corresponding parts of congruent triangles are equal]

Now, consider ΔBCE and ΔCAF,

BCE and BCA and CAF and CAB are same]

CE = AF     [From (2)]

So, from SAS congruence criterion, we have 

[Corresponding parts of congruent triangles are equal]

From (4) and (5), we have

AD= BE= CF

Median AD = Median BE = Median CF

The medians of an equilateral triangle are equal

∴ Hence proved

Related questions

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

...