Cho tam giác ABC vuông tại A. Dựng phía ngoài tam giác các hình vuông ABFG, ACKL, BCDE. Chứng minh:
a) SFBC = SABE; b) SBCDE = SABFG + SACKL
K
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CM
25 tháng 1 2017
) Ta chứng minh được DFBC = DABE (c.g.c) suy ra SFBC = SABE.
b) Đặt độ dài các cạnh BC, AC, AB lần lượt là a, b, c. Ta có SABFG = c2, SACKL = b2, SBCDE = c2.
Áp dụng dụng định lý Pytago, ta thu được ĐPCM
9 tháng 8 2015
AB < AC
Mà ABCD là hình vuông có cạnh AB ; AC tức là AB = AC => mâu thuẫn
ML
9 tháng 8 2015
Tam giác ABC vuông ở A=>AB<BC
Mà ABCD là hình vuông =>AB=BC(trái đề bài)
15 tháng 6 2022
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CM
18 tháng 1 2018
Ta có: ∠ (FAB) = ∠ (ABC) = 60 0
FA // BC (vì có cặp góc ở vị trí so le trong bằng nhau)
BC ⊥ BE (vì BCDE là hình vuông)
Suy ra: FA ⊥ BE
BC ⊥ CD (vì BCDE là hình vuông)
Suy ra: FA ⊥ CD
Gọi giao điểm BE và FA là H, FA và CG là K.
⇒ BH ⊥ FA và FH = HA = a/2 (tính chất tam giác đều)
∠ (ACG) + ∠ (ACB) + ∠ (BCD) = 60 0 + 30 0 + 90 0 = 180 0
⇒ G, C, D thẳng hàng
⇒ AK ⊥ CG và GK = KC = 1/2 GC = 1/2 AC = (a 3 )/2
S
F
A
G
= 1/2 GK.AF = 
S F B E = 1/2 FH.BE = 1/2 .a/2 .2a = 1/2 a 2 (đvdt)
CM
18 tháng 12 2019
Gọi M là trung điểm của BC, ta có:
AM = MB = 1/2 BC = a (tính chất tam giác vuông)
Suy ra MA = MB = AB = a
Suy ra ∆ AMB đều ⇒ ∠ (ABC) = 60 0
Mặt khác: ∠ (ABC) + ∠ (ACB) = 90 0 (tính chất tam giác vuông)
Suy ra: ∠ (ACB) = 90 0 - ∠ (ABC) = 90 0 – 60 0 = 30 0
Trong tam giác vuông ABC, theo Pi-ta-go, ta có: B C 2 = A B 2 + A C 2
⇒ A C 2 = B C 2 - A B 2 = 4 a 2 - a 2 = 3 a 2 ⇒ AC = a 3
Vậy S A B C = 1/2 .AB.AC
= 1 2 a . a 3 = a 2 3 2 ( đ v d t )