Proving Triangles are SimilarVideos, worksheets, stories and songs to help Grade 8 students learn how to determine if two triangles are similar.
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 Circles and Right Triangles Two triangles in a circle are similar if two pairs of angles have the same intercepted arc. Sharing an intercepted arc means the inscribed angles are congruent. Since these angles are congruent, the triangles are similar by the AA shortcut. 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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