Ai giải nhanh hộ mk vs Mk cần gấp

Mikamika

2 năm trước

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ngohoanglam2005

Đáp án:

Giải thích các bước giải:

a) Vì ABCD là hình thang nên ta có:

AB // CD (gt) (1)

$\Rightarrow \hat{D_{1}} = \hat{B_{1}}$ (2 góc so le trong) (2)

Và $\hat{C_{1}} = \hat{A_{1}}$ (2 góc so le trong) (3)

Xét $Δ I M D$ và $Δ I A B$ ta có:

$\hat{I_{1}} = \hat{I_{2}}$ (2 góc đối đỉnh) (4)

Từ (2), (4) $\Rightarrow Δ I M D \sim Δ I A B$ (G-G) (5)

Xét $Δ K M C$ và $Δ K B A$ ta có:

$\hat{K_{1}} = \hat{K_{2}}$ (2 góc đối đỉnh) (6)

Từ (3), (6) $\Rightarrow Δ K M C \sim Δ K B A$ (G-G) (7)

Từ (5) $\Rightarrow \frac{I M}{I A} = \frac{D M}{A B}$ (8)

Từ (7) $\Rightarrow \frac{K M}{K B} = \frac{M C}{A B}$ (9)

Mà DM = MC (M là trung điểm của CD) (10)

$\Rightarrow \frac{D M}{A B} = \frac{M C}{A B}$ (11)

Từ (8), (9), (11) $\Rightarrow \frac{I M}{I A} = \frac{K M}{K B}$ (12)

Nên IK // AB (định lý Ta-lét đảo) (13)

b) Từ (1), (13) $\Rightarrow$ IK // CD (14)

Từ (14) $\Rightarrow$ EI // DM, áp dụng hệ quả của định lý Ta-lét đối với $Δ A D M$ ta có:

$\frac{A I}{A M} = \frac{E I}{D M}$ (15)

Từ (14) $\Rightarrow K F$ // MC, áp dụng hệ quả của định lý Ta-lét đối với $Δ B C M$ ta có:

$\frac{B K}{B M} = \frac{K F}{M C}$ (16)

Từ (14) $\Rightarrow$ IK // MC, áp dụng hệ quả của định lý Ta-lét đối với $Δ A C M$ ta có:

$\frac{A I}{A M} = \frac{I K}{M C}$ (17)

Từ (14) $\Rightarrow I K$ // DM, áp dụng hệ quả của định lý Ta-lét đối với $Δ B D M$ ta có:

$\frac{B K}{B M} = \frac{I K}{D M}$ (18)

Từ (10) $\Rightarrow \frac{I K}{M C} = \frac{I K}{D M}$ (19)

Từ (17), (18), (19) $\Rightarrow \frac{A I}{A M} = \frac{B K}{B M}$ (20)

Từ (15), (16), (17), (20) $\Rightarrow \frac{E I}{D M} = \frac{K F}{M C} = \frac{I K}{M C}$ (21)

Từ (10), (21) $\Rightarrow E I = K F = I K$

$\Rightarrow E I = K F = I K$

Vote (0) Phản hồi (0) 2 năm trước

linhnguyenw

a , xét Δ ABI và Δ MDI có

∠BAI = ∠IDM (AB // CD)

∠ABI = ∠IDM (AB // CD)

=> Δ ABI ∞ Δ MDI (G - G)

=> AI / IM = AB / MD

cmtt có BK / MK = AB / MC

mà DM = CM (M là trung điểm của CD)

=> AI / IM = BK / MK

=> IK // AB (ta - lét đảo)

b , chứng minh tương tự như câu a có

EI // AB và KF // AB

=> EI / AB = DI / BD

KF / AB = CK / AC

mà DI / BD = CK / AC

=> EI / AB = KF / AB

=> EI = KF

cmtt có EI = IK

=> EI = KF = IK

Vote (0) Phản hồi (0) 2 năm trước

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