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are triangles that have the same size and shape. Congruent triangles ? Similar triangles ? have the same shape but different sizes. Similar Triangles ? Congruent Triangles ? How do we know when triangles are similar? Their corresponding angles have to be Their corresponding sides have to be 2 5 4 1 2.5 2 proportional ? congruent ? The triangles shown are similar. Find the ratio ofthe corresponding sides of the triangles.Simplify to a whole number if possible. 3 7.5 6 1 2.5 2 31 = The triangles shown are similar. Find the ratio ofthe corresponding sides of the triangles.Simplify to a whole number if possible. 3 7.5 6 1 2.5 2 6 2 = The triangles shown are similar. Find the ratio ofthe corresponding sides of the triangles.Simplify to a whole number if possible. 3 7.5 6 1 2.5 2 7.52.5 = These triangles are similar. Solve for x. 2 5 x 20 5x = x 2 Solve x = = 5 These triangles are similar. Solve for x. 10 6 15 x 10x = x 6 Solve x = = 10 There are three ways to prove triangles similar. Drag and drop the correct postulate abbreviation. Some drop values will not be used. Side Side Side Side Angle Side Angle Angle SSS ? SAS ? AA ? ASA AAS HL Complete the similarity statement. AA Similarity Postulate:If two angles of one triangle are congruent to two anglesof another triangle, the triangles are similar. R T S F ∆RST ~ ∆ E G The triangles shown in the picture are: )) 10 congruent by SAS congruent by ASA similar by SAS similar by SSS similar by AA 5 )) The triangles shown in the picture are: 13 12 congruent by SAS congruent by SSS similar by SAS similar by SSS similar by AA 5 5 12 13 The triangles shown in the picture are: 10 6 congruent by SAS congruent by SSS similar by SAS similar by SSS similar by AA 5 3 The triangles shown in the picture are: 10 ) 14 congruent by SAS congruent by SSS similar by SAS similar by SSS similar by AA 12 5 7 6 (( SAS Similarity Postulate: If two sides of one triangle are proportional to two sides of another triangle, and the angles between thesides are congruent, then the triangles are similar. Simplify each ratio. 8 6 12 9 12 8 9 6 = = 9 3 SSS ? 4 6 1 3 1 SAS ? 2 AA ? 12 3 |