问题 解答题

定理“直角三角形斜边上的中线等于斜边的一半”的逆命题是______,这个命题正确吗?若正确,请你证明这个命题,若不正确请说明理由.

答案

逆命题是“三角形一边上的中线是这边的一半的话,那么这个三角形是直角三角形”

这个命题是正确的.

已知:△ABC中,D是AC的中点,BD=AD,BD=DC.

求证:△ABC是直角三角形.

证明:∵BD=AD,

∴∠A=∠ABD,

∵BD=DC,

∴∠C=∠DBC,

∵∠A+∠C+∠ABD+∠DBC=180°,

∴2(∠A+∠C)=180°,

解得∠A+∠C=90°,

∴∠ABC=90°.

即△ABC是直角三角形.

选择题
阅读理解

阅读理解。

     Sitting is art that isn't getting passed along People these days feel as though they have to be doing

something If they are not working, they are jogging, or playing tennis or golf, or taking Courses to

improve their minds or bodies -or they are parked in front of the TV. Sitting in front of the TV isn't

sitting-it's watching.

     People used to sit a whole lot. You would walk down the street or drive down the road, and there

they would be, out on the doorsteps, sitting. You could go down to the store and sit on the bench out

front in the Summer or around the fire in the winter. There were sitting benches out in the town square.

At the garage, there were straight-backed chairs. There among the oilcans and tries and spare parts, you

could kick back and sit.

     Houses used to have sitting rooms, where the grown ups would go after Sunday dinner. Mom and

Dad, Grandpa and Aunt Ruby would sit and digest (消化) the fried chicken and talk about Aunt Ethel's

illness, and how well the minister did today. Outside, the children would play, and the afternoon would

pass by in a comfortable haze  (悠闲的氛围).

     That sort of thing looks like doing nothing. A recharging battery (正充电的电池) doesn't look as if

it's doing anything either. Sitting restores your soul. if you want to enjoy a truly full life, don't just do

something-sit there.

1.What message does the author try to get through to us?

A. People should make better use of their sitting room.

B. People should spend less time watching TV.

C. People should pass down their good habits.

D. People should take things easy for their own good.

2. We can learn from the second paragraph that ______.

A. people lived a more restful life in the past

B. towns were built to make living convenient

C. small town garages had a lot to offer 、

D. people enjoyed going out for a drive

3. The sitting room mentioned in the text used to be a place for ______.

A. eating food

B. watching TV

C. gathering together

D. playing with children

4. From the text we know the water believes _____.

A. sitting has a good spiritual effect

B. sitting helps people remember the past

C. sitting room may have different purposes

D. a sitting room is important for the old