Triangle angle theorems instruction active proving the sum of the interior angle measures of a triangle is 180°

Given: y║z

Using given statement:

From the figure, we have

By the definition of straight angle, .

By the angle addition postulates in we have;

The Alternate Interior Angles theorem states:

If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

Since , then by alternative interior angle theorem we have  

and

We know that : then by the substitution of and we get,

See the attached picture

Step-by-step explanation:

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

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