When triangles are similar, ratio of corresponding sides is equal.

In summary, when triangles are similar, the ratio of corresponding sides is equal and can be proven by drawing a line parallel to the base of a triangle and using the parallel postulate or by using the law of sines. This is the definition of similar triangles and does not require experimental proof.
  • #1
eightsquare
96
1
"When triangles are similar, ratio of corresponding sides is equal."

"When triangles are similar, ratio of corresponding sides is equal."

I was wondering if there is any theoretical proof for this statement or is it only experimental?
 
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  • #2
It's definition..
 
  • #3
The definition of similar triangles is the three corresponding angles have the same measure. The ratio of the sides being equal can be proven by drawing a line parallel to the base of a triangle(creating 2 similar triangles sharing one angle), and showing that the sides are proportional and the angles are the same via the parallel postulate.
 
  • #4
eightsquare said:
"When triangles are similar, ratio of corresponding sides is equal."

I was wondering if there is any theoretical proof for this statement or is it only experimental?

Haven't you taken Experimental Geometry yet?
 
  • #5
coolul007 said:
The definition of similar triangles is the three corresponding angles have the same measure. The ratio of the sides being equal can be proven by drawing a line parallel to the base of a triangle(creating 2 similar triangles sharing one angle), and showing that the sides are proportional and the angles are the same via the parallel postulate.

You can also use the law of sines.
 

Related to When triangles are similar, ratio of corresponding sides is equal.

What does it mean for triangles to be similar?

In geometry, two triangles are considered similar if their corresponding angles are congruent and their corresponding sides are in proportion.

How can you prove that two triangles are similar?

Two triangles can be proven to be similar by using the following methods: AA (angle-angle) similarity, SAS (side-angle-side) similarity, and SSS (side-side-side) similarity.

What is the importance of understanding the ratio of corresponding sides in similar triangles?

The ratio of corresponding sides in similar triangles is important because it allows us to solve for unknown side lengths and to find missing angles in the triangles.

Can you have two similar triangles with different side lengths?

Yes, as long as their corresponding angles are congruent and their corresponding sides are in proportion, two triangles can be similar even if their side lengths are different.

How does the ratio of corresponding sides in similar triangles relate to the concept of scale factor?

The ratio of corresponding sides in similar triangles is equal to the scale factor, which is the factor by which all corresponding side lengths are multiplied to get from one triangle to the other.

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