In triangle ABC, the bisectors of angle A, angle B, and angle C cut the opposite sides into lengths a1, and

Mathematics

1 answer:

Ostrovityanka [42]3 years ago

8 0

Question

In triangle ABC, the bisectors of angle A, angle B, and angle C cut the opposite sides into lengths a1, and

a2, b1, and b2, and c1 and c2, respectively, labeled in order counterclockwise around triangle ABC for

a1 = 5/3, a2 = 10/3,b1 = 15/4. Find the perimeter of triangle ABC.

Step-by-step explanation:

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cho tứ giác ABCD. Gọi M,N,P,Q là trung điểm của các cạnh AB, CD, AD, BC. Chứng minh rằng vecto MP = vecto QN, vecto MQ = vecto P

Dmitriy789 [7]

Answer:

Step-by-step explanation:

Xét tam giác DAB có: P là trung điểm AD, M là trung điểm AB

=> MP là đường trung bình của tam giác DAB => MP//BD và MP= $\frac{1}{2}$ BD (1)

Xét tam giác DBC có: N là trung điểm DC, Q là trung điểm BC

=> QN là đường trung bình của tam giác DBC => QN//BD và QN= $\frac{1}{2}$ BD (2)

Từ (1) và (2) => vecto MP song song cùng chiều với vecto QN

và độ dài MP = độ dài QN = $\frac{1}{2}$ BD

=> vecto MP = vecto QN

Tương tự xét các tam giác DAC và tam giác ABC => vecto MQ = vecto PN

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