If we split a line segment into two segments, the length of the total segment equals the sums of the lengths of the two smaller segments. We can make an equation out of the given information.

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Given the sum of a pair of angle measures and the algebraic expressions that represent them, form and solve an equation. Includes complementary, supplementary, and other adjacent angles.

Given an information about the lengths of line segments, form and solve an equation in order to find the lengths of the segments.

Using similarity, we can prove the Pythagorean theorem and theorems about segments when a line intersects 2 sides of a triangle.

Because we've shown that if x is equal to y, there's no way for l and m to be two different lines and for them not to be parallel. And so we have proven our statement.

We know that segment AC is congruent to segment AC, it sits in both triangles, and this is by reflexivity, which is a fancy way of saying that something is going to be congruent to itself.

I would suggest instead rerecording that segment with an edited correction. So often I wish we could shorten the videos by eliminating rewriting to change colors or to correct previous …

The idea that "if x=y, and y=z, then z=x" goes along with the transitive property of equality even though they are letters supports the idea that angles can be assigned numbers with proof that …

The postulate used in this video, as Joshua mentioned, is AAS (Angle-Angle-Side). This is a known, valid postulate - the proof and explanation of which is available in earlier videos in this …