Math Is Fun Forum

Hannibal lecter

Member

Registered: 2016-02-11

Posts: 392

How to Find if Triangles are Similar

on MIF https://www.mathsisfun.com/geometry/triangles-similar-finding.html

in the SAS example "side, angle, side"
there is two triangles, he found that these two is similar 
because thier ratios are equal
21 : 14  which is 3/2
and
15 : 10 which is 3/2

my problem is he divide Traingle1 Side over Traingle two Side
and divide the second side which is 15 of traingle 1 when the second side of the traingle two which is 10

but in Similar Topic on MIF https://www.mathsisfun.com/geometry/similar.html

in the Example named " Example: What is the missing length here?"
he divided the blue triangles with its sides themselves : 130/127 which is blue traingle side over blue traingle second side
and equal to  ?/80 which is red side over red side

now how to check the similarity exactly by dividing one side of a traingle with the other traingle side? or using the same side of the traingle
for example traingle with side x1 and x2 and another traingle with side y1 and y2
the similarity check is using : x1 over y1 equal to x2 over y2
or : x1 over x2 equal to y1 over y2?

Last edited by Hannibal lecter (2023-08-31 22:26:16)

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Wisdom is a tree which grows in the heart and fruits on the tongue

Bob

Administrator

Registered: 2010-06-20

Posts: 10,184

Re: How to Find if Triangles are Similar

In the first example the 75 angle is not in the 'same' position in both triangles.  You have to expect this.  Two triangles can be similar; if you turn one round a bit, they're still similar.

To work out which sides to use to make the ratio look carefully at the sides making the angle of 75.  In one triangle it is 15 and 21; in the other it is 14 and 10.  Now it must be the smaller sides that go to make a ratio, and the longer sides to make a ratio.  Two triangles would never be similar if long and short were put together.

So make the ratios out of 15 and 10 for one; and 21 and 14 for the other.

15/10  and 21/14

In the second example we know the triangles are similar because they share the acute angle on the left and they both have a 90 angle.  So similar AA.

Now to identify which sides in the red triangle have been scaled up to make the blue triangle. ? and 130 are the hypotenuse for each triangle.  The sides adjacent to the acute angle are 80 and 127.

So think of the question like this.  The 127 has been scaled down to 80.  That's equivalent to multiplying 127 by 80/127.

So the unknown side, ? , must be scaled down by the same fraction:

? = 130 x 80/127

Hope that helps,

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob