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Transcript
C ONGRUENT F IGURES If you can flip, rotate, or move one shape to fit exactly on another, the shapes are congruent. Two figures are congruent if they are the same size and shape. C ONGRUENT VS N OT C ONGRUENT The two shapes to the right are congruent: The two shapes to the right are NOT congruent: Corresponding Parts By Definition if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. 1. AB ≅ DE 2. BC ≅ EF 3. AC ≅ DF 4. ∠ A ≅ ∠ D 5. ∠ B ≅ ∠ E 6. ∠ C ≅ ∠ F ∆ABC ≅ ∆ DEF Do you need all six ? NO ! SSS SAS ASA AAS R ULES FOR C ONGRUENT T RIANGLES SSS – Side, Side, Side Rule If the three sides of a triangle are congruent to the three sides of another triangle, then the two triangles are congruent. R ULES FOR C ONGRUENT T RIANGLES SAS – Side Angle Side Rule If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. Included angle = angle created by two sides of a triangle. R ULES FOR C ONGRUENT T RIANGLES ASA – Angle Side Angle Rule If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then these two triangles are congruent. Included side = a side that is common between two angles. R ULES FOR C ONGRUENT T RIANGLES AAS – Angle Angle Side If two angles and a non- included side of a triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the two triangles are congruent. Example R ULES FOR C ONGRUENT T RIANGLES HYPOTENUSE-LEG This rule can only be used with right triangles (triangles that have one angle measuring 90°). It states if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent. S IMILAR F IGURES Two shapes are similar if their corresponding angles are equal and their corresponding line segments are proportional. S IMILAR F IGURES Here are two similar shapes. Make a statement about the corresponding angles, using a vocabulary word from today’s lesson in the chat box. Are these figures similar? Example 1 If we have a triangle with side lengths of 2, 3, and 4 and a larger similar triangle with the shortest side equal to 6, what is the length of the other two sides of the triangle? x n 4 3 2 6 Example 1: If we have a triangle with side lengths of 2, 3, and 4 and a larger similar triangle with the shortest side equal to 6, what is the length of the other two sides of the triangle? 4 3 2 x n 6 Solution: Since the shortest side of the first triangle is 2, we know that 2 x 3 is 6, so the other sides are 3 times the sides of the first triangle. The other two sides are 9 and 12 (3 x 3 = 9 and 4 x 3 = 12).