State the triangle similarity theorem that proves the triangles are similar.

Question

jlo2niT · Accepted Answer

Step 1
In geometry, two shapes are similar if they are the same shape but different sizes.
Similar triangles are easy to identify because you can apply three theorems specific to triangles. These three theorems, known as Angle - Angle (AA), Side - Angle - Side (SAS), and Side - Side - Side (SSS).
Angle-Angle (AA) says that two triangles are similar if they have two pairs of corresponding angles that are congruent. The two triangles could go on to be more than similar. they could be identical. For AA, all you have to do is compare two pairs of corresponding angles.
Step 2
SAS (Side-Angle-Side)
If two pairs of corresponding sides are in proportion, and the included angle of each pair is equal, then the two triangles they form are similar. Any time two sides of a triangle and their included angle are fixed, and then all three vertices of that triangle are fixed. With all three vertices fixed and two of the pairs of side’s proportional, the third pair of sides must also be proportional.
SSS (Side-Side-Side)
Another way to prove triangles are similar is by SSS, side-side-side. If the measures of corresponding sides are known, then their proportionality can be calculated. If all three pairs are in proportion, then the triangles are similar.
Step 3
In the given figure,
Both triangles are similar by SSS theorem, because all three pairs are in proportion,
To calculate the proportion of sides,

\frac{15}{24} = \frac{5}{8}

\frac{8}{12.8} = \frac{80}{128}

= \frac{5}{8}

\frac{10}{16} = \frac{5}{8}

Hence the proportion of sides is (

\frac{5}{8}

) therefore both triangles are similar.

State the triangle similarity theorem that proves the triangles are similar.

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