In triangle ABC AB = 15 cm, АС = 20 cm. On the side AB there is a segment AD = 8 cm, and on the side

| May 4, 2021 | education

In triangle ABC AB = 15 cm, АС = 20 cm. On the side AB there is a segment AD = 8 cm, and on the side АС there is a segment AE = 6 cm. A) Are triangles ABC and ADC similar and why; b) prove that triangles ABC and AED are similar, and find BC if DE = 12 cm; c) find the height of the AK if DE = 10 cm.

AB = 15 cm, AC = 20 cm; AD = 8; AE = 6 cm.

1) Consider the similarity of triangles ABC and ADC. Angle <And they have a common, AB / AC = 15/20 = 3/4; AD / AB = 8/20 = 2/5. Since the two sides are not proportional and the angle is equal, the triangles are not alike.

2) Triangles ABC and ADE. Angle <And they have a common, AB / AC = 15/20 = 3/4; AE / AD = 6/8 = 3/4. Since the two sides are proportional and the angle is equal, the triangles are similar.

3) Find the side BC: BC / DE = AC / AD = 20/15 = 4/3; then BC = DE * 4/3 = 12 cm * 4/3 = 16 cm.



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