BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles.
Triangles
1
Posts
2
Users
0
Likes
487
Views
0
12/07/2021 12:05 pm
Topic starter
BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles.
Answer
Add a comment
Add a comment
1 Answer
0
12/07/2021 12:06 pm
It is known that BE and CF are two equal altitudes.
Now, in ΔBEC and ΔCFB,
BEC = CFB = 90° (Same Altitudes)
BC = CB (Common side)
BE = CF (Common side)
ΔBEC ΔCFB by RHS congruence criterion.
C = B (by CPCT)
Therefore, AB = AC as sides opposite to the equal angles is always equal.
Add a comment
Add a comment
Forum Jump:
Related Topics

Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
3 years ago

In Figure, PR > PQ and PS bisect QPR. Prove that PSR > PSQ.
3 years ago

AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD (see Figure). Show that A > C and B > D.
3 years ago

In Figure, B < A and C < D. Show that AD < BC.
3 years ago

In Figure, sides AB and AC of ΔABC are extended to points P and Q respectively. Also, PBC < QCB. Show that AC > AB.
3 years ago
Forum Information
 321 Forums
 27.3 K Topics
 53.8 K Posts
 1 Online
 12.4 K Members
Our newest member: Stripchat
Forum Icons:
Forum contains no unread posts
Forum contains unread posts
Topic Icons:
Not Replied
Replied
Active
Hot
Sticky
Unapproved
Solved
Private
Closed