what is the proof -corresponding altitudes of similar triangles have the same ratio as the corresponding sides

Question

I need to know how to do the proof for that.... Corresponding altitudes of any two similar triangles have the same ratio as the corresponding sides

Answer 1

Take a look at these triangles. Lets say they're similar.
Let the first one be ABC and the smaller one be DEF
a/\
/ \ d
b/__\ c e/\f

let's draw the altitudes
a/|\
/ | \ d
b/_|_\ c e/|\f
m n

Each form more two little triangles. Because Therefore, the ratio of the length of am and dn is the same as the ration of ac and df. Therefore, the ration of the length of am and dn is the same as the other lengths.

I hope you understood.

Answer 2

let ABC and DEF are similar triangles.

let A = D, B = E, C = F

then AB and DE, BC and EF, AC and DF are corresponding sides

draw altitudes AM from A to BC and DN from D to EF.

in triangle ABC

sinB = AM/AB

AM = AB sin B ------------eqn(1)

in triangle DEF

sin E = DN/DE

DN = DE sin E ---------------eqn(2)

divide eqn(1) by eqn(2)

AM/DN = AB sin B/DE sin E

but sin B = sin E

so AM/AN = AB/DE

so in similar triangles altitudes have the same ratio as corresponding sides

Answer 3

The triangles formed by the altitudes and a side and part of a 3rd side are also similar to each other because of AA where the right angles are equal and the acute angles are equal.

Hence h1/h2 = s1/s2

Answer 4

Side Angle Side (SAS) Postulate:
If there is a correspondence between the vertices such that two sides and the included angle are isometric then the triangles are isometric. Moreover, both could be built or rebuilt by the same construction SAS method and each may be moved to be coincide with the other by a sequence of translations, rotations and/or reflections.

or

Angle Side Angle (ASA) Postulate:
If there is a correspondence between the vertices such that two angles and the included side are isometric then the triangles are isometric. Moreover, both could be built or rebuilt by the same construction ASA method and each may be moved to be coincide with the other by a sequence of translations, rotations and/or reflections.

Answer 5

seems like an Angle-Side-Side (A S S) to me

Answer 6

So what would be the correctly stated given then??

Answer 7

Umm i graduated and didnt learn that.... :(