Дано: АВCD - трапеции, АВ и CD - боковые стороны трапеции АВ =10, CD = 26, ВС = 1, DM - биссектриса ∠ADC проходящая через середину АВ.
Найти: S - ?
Решение.
Проведем через точку М линию MN ║ AD, т.к. АМ=МВ= 10 / 2 = 5 по условию задачи, то MN - средняя линия.
DM - биссектриса, то ∠ADM = ∠MDC, а ∠NMD = ∠ADM как накрест лежащие при параллельных прямых (MN ║ AD), отсюда следует, что ∠NMD = ∠NDM следовательно ΔMND - равнобедренный. (смотри рисунок ниже) тогда MN = ND = CD / 2 = 26 / 2 = 13
С другой стороны средняя линия в трапеции равна
Проведем в равнобедренном треугольнике ΔMND прямую NO - высоту и продлим эту прямую до точки К лежащей на прямой AD. ΔNOD = ΔKOD - по стороне (OD) и двум прилежащим к ней углам, следовательно MNDK ромб, у которого MK = MN = ND = KD = 13 тогда AK = AD - KD = 25 - 13 = 12
Если в ΔAMK выполняется условие MK² = AM² + AK² , то ΔAMK - прямоугольный. 13² = 5² + 12² 169 = 169 , следовательно ∠MAK = 90° , а трапеция ABCD прямоугольная, Тогда высота трапеции равна h = AB = 10
After each term in school we had our holidays. It's fun to have holidays, you can do whatever you like, you don't have to get up too early, do your homework or think of troubles which occur very often at school.Most of all I liked summer holidays, they were the longest ones, though, when winter was snowy and and frosty, I enjoyed my winter holidays skating and skiing, sledging and making a snowman or having a fight with snowballs.I'd like to tell you about my summer holidays I spent in Sochi. It was just three years ago. My parents and me were sitting in the living-room discussing our plans for the summer holidays. My father suggested that we should go to Sochi. On hearing that I jumped up with joy and said it was a wonderful idea. My mother wasn't against the idea either. So one summer morning we started for our journey to Sochi.First, we travelled to Odessa by plane and from there we got to Sochi by boat. We stayed in Odessa for three days, our relatives live there and they gave us board and lodging. So we had an excellent opportunity to go round the city, to see beautiful monuments to the famous people who had lived in Odessa, museums and the Odessa Opera House.We enjoyed our trip from Odessa to Sochi. The Black Sea was calm. We sat on deck in the lounge chairs and looked at the sea. I like Sochi very much, we bathed and went boating and swimming, lay in the sun on the beach. In the evenings we went for a walk or dropped in at a cafe to have ice-cream or juice.My father showed us the famous Botanical Gardens, we went for hikes in the mountains, we saw the magnificent Augura Waterfalls. The sea was nice and warm. The weather was fine. When it was time to go home, we were sorry to leave the marvellous town of Sochi.
кв.ед.
300 и 30
30=30