Reading (5 points)
Task 1. Read the text:
Nowadays people have started to realize that good health is very important. much more important than
wealth. To be in good health people must follow a healthy life style to do things that will help keep a
healthy body and mind, to feel fit. There are several ways to do it. The state of your body depends on how
much time you spend doing sports. At least everybody must do moming exercises every day. The healthiest
kinds of sports are swimming, running and cycling. Healthy food is also a very important factor. The daily
menu should include meat, fruit and vegetables, milk product, which are rich in vitamins, fax, proteins and
etc. On the other hand modem diets are very popular especially among women. Diets may be harmful, if
they are used in the wrong way. To be healthy, people should get rid of their bad habits. It's necessary to stop
smoking and drinking much. Everyone should remember that citarettes, alcohol and drugs destroy both
body and brain. In addition it is recommended to watch TV less, avaid anxiety and observe daily routine.
Read the statements and choose T (True), F (False )or DS (doesn't say)
1)Good health is very significant.
2)All diets are useful and healthy.
3)It is recommended to do yoga to be in good health.
4) Alcohol and cigarettes influence only on body.
5)It is important to get rid of bad habits in order to keep a healthy body and mind.
Медианы ЕN и FM треугольника EFK, длины которых 12 и 18, пересекаются под прямым углом. Найдите площадь Треугольника EFK.
Объяснение:
1) Рассмотрим выпуклый четырёхугольник EFNM у которого диагонали , по условию, взаимно- перпендикулярны .
Его площадь можно найти по формуле S = 1/2*d₁*d₂* sin (∠d₁d₂).
S(EFNM) = 1/2*12*18* sin 90°=108 ( ед²).
2) S(EFK)=S(EFNM)+S(MNK)
3) MN-средняя линия , тк M,N-середины сторон по определению медианы . По т. о средней линии треугольника MN║EF .
ΔEFK ∼ΔMNK по 2-м углам : ∠К -общий ,∠FEK=∠NMK как соответственные при MN║EF ,секущей ЕК ⇒ сходственные стороны
пропорциональны
, k=
. По т об отношении площадей
подобных треугольников
или 
,
4*S( MNK)=S(MNK)+S(EFNM) ,
3(MNK)=108 , S(MNK)=36 ед².
4) S(EFK)=S(EFNM)+S(MNK) =108+36=144 ( ед²).