SOLUTION: How can i explain how triangles are similar and how do i solve for missing lengths

Question 1002024: How can i explain how triangles are similar and how do i solve for missing lengths
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52784)   (Show Source): You can put this solution on YOUR website!
.
You need to know the definition of similarity for triangles and the tests for triangles similarity.

See, for example, the lessons

    - Similar triangles,
    - Similarity tests for triangles,
    - Proofs of Similarity tests for triangles,
    - Problems on similar triangles,
    - Problems on similarity for right-angled and acute triangles,
    - Miscellaneous problems on similar triangles
    - Solved problems on similar triangles
    - OVERVIEW of lessons on similar triangles.

Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

Two triangles are if they have:
all their angles equal
corresponding sides are in the same ratio
But we don't need to know all three sides and all three angles; two or three out of the six is usually enough.
There are three ways to find if two triangles are similar:
, and
stands for "angle, angle" and means that the triangles have two of their angles equal (could also be called because when two angles are equal, all three angles must be equal).
If two of their angles are equal, then the third angle must also be equal, because angles of a triangle always add to make �.
example: if one angle is � and second angle is �, the third
will be �

stands for "side, angle, side" and means that we have two triangles where:
the ratio between two sides is the same as the ratio between another two sides
and we we also know the included angles are equal
If two triangles have two pairs of sides in the same ratio and the included angles are also equal, then the triangles are similar.
example:
one pair of sides is in the ratio of
another pair of sides is in the ratio of
there is a matching angle of � in between them
So there is enough information to tell us that the two triangles are similar.

stands for "side, side, side" and means that we have two triangles with all three pairs of corresponding sides in the same ratio.
If two triangles have three pairs of sides in the , then the triangles are similar.
example:
the ratios of sides are:

These ratios are , so the two triangles are similar.
Since the ratios of the lengths of corresponding sides of similar figures are equal, then use this idea to find missing segment lengths in similar figures.

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