Similar Triangles
Posted: Thu Jun 04, 2015 3:05 pm
Similar Triangles requirements:
*Two sides have lengths in the same ratio, and the angles included between these sides have the same measure
*Two right triangles are similar if the hypotenuse and one other side have lengths in the same ratio.
(Copied from Wikipedia)
Why do we need "the angles included between these sides"? an angle, Opposite side of that angle and another side having lengths in the same ratio also should make both triangles similar. But I don't find this condition anywhere. Everywhere there is only 3 conditions: Angle-Angle, Side-Angle-Side, SSS (and right angle ext.). Why nowhere there is a mention of "an angle, Opposite side of that angle and another side having lengths in the same ratio?" Doesn't this make two triangles similar? Am I missing something?
ref: http://goo.gl/9HSfD http://goo.gl/fAsX1
*Two sides have lengths in the same ratio, and the angles included between these sides have the same measure
*Two right triangles are similar if the hypotenuse and one other side have lengths in the same ratio.
(Copied from Wikipedia)
Why do we need "the angles included between these sides"? an angle, Opposite side of that angle and another side having lengths in the same ratio also should make both triangles similar. But I don't find this condition anywhere. Everywhere there is only 3 conditions: Angle-Angle, Side-Angle-Side, SSS (and right angle ext.). Why nowhere there is a mention of "an angle, Opposite side of that angle and another side having lengths in the same ratio?" Doesn't this make two triangles similar? Am I missing something?
ref: http://goo.gl/9HSfD http://goo.gl/fAsX1