The Third Angle Theorem (Tat): Discover A Powerful Tool To Find & Prove Triangle Angles Congruency

Third Angle Theorem (TAT)

if two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent

The Third Angle Theorem (TAT) relates to how the angles of a triangle are related to each other. It states that the measure of the third angle of a triangle is equal to the difference between 180 degrees and the sum of the other two angles in the triangle. In other words, if we have a triangle with angles A, B, and C, then:

C = 180 – (A + B)

This theorem is based on the fact that the sum of the measures of the angles of a triangle is always 180 degrees. So, when we subtract the sum of the other two angles from 180 degrees, we get the measure of the third angle.

The TAT is important because it can be used to find the measure of an angle in a triangle if the other two angles are known. Additionally, it can be used to prove that two triangles are congruent if their corresponding angles are equal.

To use the TAT to solve for an unknown angle, simply plug in the measures of the other two angles and simplify the equation. For example, if we have a triangle with angles A= 40 degrees and B = 60 degrees, we can find the measure of angle C as follows:

C = 180 – (40 + 60)
C = 80 degrees

Therefore, angle C in this triangle measures 80 degrees.

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