Question

Which reason is missing in step 2? CPCTC definition of supplementary angles triangle parts relationship theorem triangle angle sum theorem.

Answer 1

The reason which is missing from the step 2 in the calculation of two similar triangle, is triangle angle sum theorem.

What is triangle angle sum theorem?

According to the triangle angle sum theorem, the sum of all the angle(interior) of a triangle is equal to the 180 degrees.

Given information-

The measure of the angle in the given problem is as,

$m\angle H=30^o\\m\angle J=50^o\\m\angle P=50^o\\m\angle N=100^o$

The two triangle has to be prove similar as,

$\Delta HKJ \sim\Delta LNP$

The image of the two triangle attached below.

The calculation done in the second step is as,

$m\angle H +m\angle J+m\angle K=180$

In the above calculation all the angle of the first triangle are added together. The result of the sum of all the angle of the triangle kept equal to the 180.

This is done by the property of triangle angle sum theorem, which says the sum of all the angle(interior) of a triangle is equal to the 180 degrees.

Thus the reason which is missing from the step 2 in the calculation of two similar triangle, is triangle angle sum theorem.

Learn more about the triangle angle sum theorem here;

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