Home > Shapes > Geometry
| two2one (Posted on 2010-10-27) |
 |
Let AD be an altitude of triangle ABC.
Prove the following:
If /B = 2 /C < 90°, then |AB| + |BD| = |DC|.
Solution
|
 | Comment 1 of 2
|
Let B’ be a point on CD such that |DB’| = |DB|.
/CAB’ = /AB’D - /C (Exterior angle of triangle)
= /B - /C (Triangles ABD, AB’D congruent)
= 2 /C - /C
= /C
Therefore triangle AB’C is isosceles and |AB’| = |B’C|.
Hence |AB| + |BD| = |AB’| + |B’D|
= |B’C| + |B’D|
= |DC|
|
|
Posted by Harry
on 2010-10-27 18:54:58 |
|
|
Please log in:
Forums (0)
Newest Problems
Random Problem
FAQ |
About This Site
Site Statistics
New Comments (12)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On
Chatterbox:
|
