Section 11.2: Similar Triangles
There are four triangle congruence shortcuts: SSS, SAS, ASA, and AAS. We have triangle similarity if (1) two pairs ofangles are congruent (AA) (2) two pairs of sides are proportional and the included angles are congruent (SAS), or (3) if three pairs of sides are proportional (SSS). Notice that AAA, AAS, and ASA are not listed -- to include them would be redundant since they all have two congruent angles.
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.
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.
Notes and Powerpoints
lesson_11.2.pdf | |
File Size: | 41 kb |
File Type: |