# Proving Triangles are Similar

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Examples, solutions, videos, worksheets, stories, and lessons to help Grade 8 students learn how to determine if two triangles are similar.

Triangle Similarity - AA SSS SAS & AAA Postulates
Proving Similar Triangles, Two Column Proofs
How to use two column proofs in order to prove if two triangles are similar using the mostly the AA postulates.
Other triangle similarity postulates mentioned are the AAA, SSS, and SAS postulates. Theorems used in this video include the base angle theorem, theorems associated with parallel lines, alternate interior angle theorem, vertical angles, reflexive property, definition of an altitude, right angle congruence, and more.
Similar Triangle Proofs
Students learn that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar (Angle-Angle Similarity Postulate, or AA Similarity Postulate). Students also learn that the scale factor is ratio of the lengths of two corresponding sides. Students are then asked to use these concepts to determine whether given triangles are similar, and to find the missing side lengths in similar triangles.

Proving Triangles are Similar
Students learn the following theorems related to similar triangles.
Similar Triangles in Right Triangles
If an altitude is drawn from the right angle in a right triangle, three similar triangles are formed, also because of the AA shortcut.

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