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Download 7.1 - Congruence and Similarity in Triangles
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Transcript
Congruent Triangles When 2 triangles are congruent, they will have exactly the same three sides and exactly the same three angles. The small, blue triangle is made using the middle of each side of the large, black triangle. Are the four small triangles congruent? Are there similar triangles in this design? Yes, all the small triangles are similar to the large, black one. Create a triangle that is similar but not congruent to βπ΄π΅πΆ. SIMILAR: same angles CONGRUENT: same angles and sides So our triangle must have the same angles as βπ¨π©πͺ but different sides. A 3.3 cm A 60o 6.6 cm B 4.8 cm 60o C 7.4 cm B 2.4 cm C 3.7 cm Is βπ·πΈπΉ similar to βπ΄π΅πΆ? A 3.3 cm D B 2.4 cm 1.2 cm F 60o 1.5 cm 60o 3.7 cm C E The sides are not proportional, so the triangles are not similar. D 6.0 cm 3.6 cm C E 8.0 cm y B x A To find x, set up a proportion: π΄π΅ π΅π· = πΈπΆ πΆπ· Show that the two triangles in this diagram are similar. Then determine the values of x and y. Angle BAD = Angle CED Angle ABD = Angle ECD So, βABD ~ βECD (they are similar) To find y, set up a proportion: π΄π· π΅π· = πΈπ· πΆπ· π₯ 14.0 = 6.0 6.0 π¦ + 3.6 14.0 = 3.6 6.0 14.0 π₯ = 6.0 6.0 14.0 π¦ = 3.6 β 3.6 6.0 π = ππ. π π = π. π If two triangles are congruent, then they are also similar If two triangles are similar, they are not always congruent If two pairs of corresponding angles in two triangles are equal, then the triangles are similar If in addition two corresponding sides are equal, then the triangles are congruent