问题 选择题

在等边△ABC所在平面内找出一个点,使它与三角形中的任意两个顶点所组成的三角形都是等腰三角形.这样的点一共有(  )

A.1个

B.4个

C.7个

D.10个

答案

在等边△ABC中,三条边上的高交于点O,

由于等边三角形是轴对称图形,三条高所在的直线也是对称轴,也是边的中垂线,点O到三个顶点的距离相等,△ADB,△BOC,△AOC是等腰三角形,则点O是满足题中要求的点,

高与顶角的两条边成的锐角为30°,以点A为圆心,AB为半径,做圆,延长AO交圆于点E,

由于点E在对称轴AE上,有EC=EB,AE=AC=AB,△ECB,△AEC,△ABE都是等腰三角形,点E也是满足题中要求的点,

作AD⊥AE交圆于点D,则有AC=AD,AD=AB,即△DAB,△ADC是等腰三角形,点D也是满足题中要求的点,同理,作AF⊥AE交圆于点F,则点F也是满足题中要求的点;

同理,以点B为圆心,AB为半径,做圆,

以点C为圆心,AB为半径,做圆,都可以分别得到同样性质的三个点满足题中要求,

于是共有10个点能使点与三角形中的任意两个顶点所组成的三角形都是等腰三角形.

故选D.

多项选择题
完形填空

第二节:完形填空(共20小题;每小题1.5分,满分30分)

阅读下面短文,掌握其大意,然后从36~55各题所给的四个选项(A、B、C和D)中,选出最佳选项。

The beginning of a Frank Sinatra song drifted across the dance floor and I knew my dad would call out and request that, which for most people is very   36  .

As he walked towards me to ask for the first   37  , I could see there were   38  in his eyes .I grasped the side of my chair,   39  myself up with my arms ,and grabbed the two metal sticks which keep me   40  as I stood to take his hand.

It took all my will to   41   my own tears and inside a voice kept   42  : “Don’t fall over ,Martine.” We grabbed each other and in some way shuffled(穿梭)out a dance for the whole of the song.

For my dad, it was a turning point. He had   43   his friends on his 70th birthday he would lead his daughter in the first dance,   44   he had done so many times before .Almost a year after the suicide bomb on the London Underground train which blew   45  both my legs above the knee ,I had managed to realize his  46   .Like so much that has happened over the last 12 months, there was something   47  about the moment.

Today, on July 1, as I face the first anniversary of the terrorist   48  , I am preparing to leave the country for a while. I know I   49   be celebrating the fact that I am alive,   50  I do not feel able to remain in London for the event.

Psychologically, I am a different person. I am very body conscious. When I go out I am   51   that children will make fun of me on my artificial legs. In my wheelchair I cover my lower half with a blanket   52   what remains of my body draws   53   glances.

Despite my brave claims of what I would do when I left the hospital in March, the reality is that I will   54  be able to do many things .I thought I would be able to wear my artificial legs all day ,to run ,to go out alone. But that is just not possible.

I keep asking myself,    55   does it become normal? Is this normal now?

36.A.believable     B.difficult       C.interesting     D.simple

37.A.permission       B.dance              C.action          D.time

38.A.smiles         B.hopes          C.tears         D.sorrows

39.A.took         B.carried         C.raised          D.turned

40.A.balanced      B.supplied       C.experienced      D.equipped

41.A.keep up       B.hold back     C.put away      D.send off

42.A.saying         B.concluding       C.ringing        D.suggesting

43.A.persuaded     B.permitted     C.pleased        D.promised

44.A.so            B.but           C.as             D.while

45.A.away         B.down         C.over         D.out

46.A.attempt        B.effort              C.decision       D.dream

47.A.positive       B.unreal          C.pleasant       D.true

48.A.attacks         B.activities      C.accidents      D.situations

49.A.could              B.should         C.must         D.might

50.A.and          B.or            C.but           D.while

51.A.astonished     B.guilty          C.puzzled        D.scared

52.A.in time        B.on purpose       C.in case         D.in need

53.A.continuous       B.steady          C.angry              D.curious

54.A.never              B.seldom        C.nearly          D.almost

55.A.whether       B.when         C.why         D.where