In A ABC, seg MN | side AC. Seg MN divide triangle ABC into two parts equal in area. Determine AM/MB.
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Answer:
segment MN ║ BC
∠AMN=∠ABC (corresponding angle)
∠ANM=∠ACB (corresponding angle)
∠A si common
so ΔABC≅ΔAMN (CPCT)
given that 2*(area of ΔAMN )= area of ΔABC
so
\begin{lgathered}\frac{AM}{MB}=\sqrt{\frac{area of ABC}{area of AMN}}\\\\\frac{AM}{MB}=\sqrt{\frac{2}{1}}\\\\\frac{AM}{MB}=\sqrt{2}\end{lgathered}
MB
AM
=
areaofAMN
areaofABC
MB
AM
=
1
2
MB
AM
=
2
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