《2025年快乐过暑假江苏凤凰科学技术出版社八年级提优版》

4. 如图,在 $ \triangle ABC $ 中,$ \angle A = 50^{\circ} $,$ \angle B = 80^{\circ} $,观察图中尺规作图的痕迹,则 $ \angle DCE $ 的度数为______$ 65 ^ { \circ } $。

答案： $ 65 ^ { \circ } $

5. 如图,在 $ \text{Rt} \triangle ABC $ 中,$ \angle C = 90^{\circ} $,$ AC = 8 $,$ BC = 4 $,线段 $ PQ = AB $,$ P $、$ Q $ 两点分别在线段 $ AC $ 和过点 $ A $ 且垂直于 $ AC $ 的射线 $ AX $ 上运动,当 $ \triangle ABC $ 和 $ \triangle PQA $ 全等时,$ AP $ 的长为______4 或 8。

答案： 4 或 8

6. 如图,要使一个七边形木架不变形,至少要再钉上4根木条。

答案： 4

7. 如图,在 $ \triangle ABC $ 与 $ \triangle DBC $ 中,$ AB = DB $,$ \angle A = \angle D = 90^{\circ} $。
(1) 求证：$ \triangle ABC \cong \triangle DBC $；
证明：$ \because \angle A = \angle D = 90 ^ { \circ } $，
$ \therefore \triangle A B C $ 和 $ \triangle D B C $ 都是直角三角形.
在 $ R t \triangle A B C $ 和 $ R t \triangle D B C $ 中，$ \left\{ \begin{array} { l } { A B = D B }, \\ { B C = B C }, \end{array} \right. $
$ \therefore R t \triangle A B C \cong R t \triangle D B C $(HL).
(2) 当 $ \angle BCD = 55^{\circ} $ 时,求 $ \angle ABD $ 的度数。
解：$ \angle A B D = $$70^{\circ}$.

答案：
(1) $ \because \angle A = \angle D = 90 ^ { \circ } $，
$ \therefore \triangle A B C $ 和 $ \triangle D B C $ 都是直角三角形.
在 $ R t \triangle A B C $ 和 $ R t \triangle D B C $ 中，$ \left\{ \begin{array} { l } { A B = D B }, \\ { B C = B C }, \end{array} \right. $
$ \therefore R t \triangle A B C \cong R t \triangle D B C ( H L ) $.
(2) $ \angle A B D = 70 ^ { \circ } $.

一 选用方框内的单词或词组填空,其中有一个单词或词组是多余选项
movie advertisements store at most fall biscuit
1. There were at most twenty people in the classroom.
2. Let’s go to see the movie this afternoon.
3. The new store will be open in the spring.
4. We all like watching TV with fewer advertisements.
5. I don’t like eating this kind of biscuit.

答案： 1. at most 2. movie 3. store 4. advertisements 5. biscuit

二 阅读短文,从短文后A至F六个选项中选出五个可以填入空白处的最佳选项
My ideal school starts at 9 a. m. and finishes at 3 p. m. 1FWe have lots of time for after-school activities. We don’t have to spend lots of time on homework. We only have an hour of homework every day.
We have an hour for lunch. There is a big clean dining hall. 2CWe listen to music at lunchtime. We wear school uniforms, but we do not wear ties.
Our classes are quite small. There are about 20 students in each class. 3AI have Maths because Maths is very interesting. I love computers, so I have computer lessons.
There is a big library in our school. 4DI can borrow ten more books each time.
There is a football field. We can play football with our classmates after school. And there is a swimming pool. 5EWe can do all kinds of sports on it.
We have lots of clubs and after-school activities. Every month, we go on a school trip. We always have fun.
1. ____ 2. ____ 3. ____ 4. ____ 5. ____
A.We can choose subjects to study.
B.I always like swimming in a lake.
C.We have lunch and chat there.
D.There are all kinds of books in it.
E.There is a big playground too.
F.We do not need to get up early.

答案： 1~5 FCADE