《2025年快乐过暑假江苏凤凰科学技术出版社七年级提优版》

3. 如图,下列条件中不能判定$AB// CD$的是(A).

A.$\angle 1= \angle 2$
B.$\angle 3= \angle 4$
C.$\angle 3+\angle 5= 180^{\circ }$
D.$\angle 2= \angle 3$

答案： 3. A

4. 当光线从空气斜射入水中时,传播方向会发生改变. 如图,水面 MN 与水底 PQ 平行,光线从 A 出发,经过水面点 B 折射到水底 C 处,若 BD 为 AB 的延长线,$\angle ABN= 42^{\circ },\angle DBC= 14^{\circ }$,则 $\angle BCQ$的大小为56$^{\circ }$.

答案： 4. 56

5. 如图,在三角形 ABC 中,点 D,E 分别在 AB,BC 上,且$DE// AC,\angle 1= \angle 2$.
(1)AF 与 BC 平行吗？为什么？
答：AF//BC。理由如下：
$ \because DE // AC $, $ \therefore \angle 1 = \angle C $.
$ \because \angle 1 = \angle 2 $, $ \therefore \angle C = \angle 2 $, $ \therefore AF // BC $.
(2)若 AC 平分$\angle BAF,\angle B= 36^{\circ }$,求$\angle 1$的度数.
答：72°

答案： 5.
(1) $ AF // BC $. 理由如下：
$ \because DE // AC $, $ \therefore \angle 1 = \angle C $.
$ \because \angle 1 = \angle 2 $, $ \therefore \angle C = \angle 2 $, $ \therefore AF // BC $.
(2) $ \because AF // BC $, $ \therefore \angle B + \angle BAF = 180^{\circ} $.
$ \because \angle B = 36^{\circ} $, $ \therefore \angle BAF = 144^{\circ} $.
$ \because AC $ 平分 $ \angle BAF $, $ \therefore \angle 2 = \frac{1}{2} \angle BAF = 72^{\circ} $.
$ \because \angle 1 = \angle 2 $, $ \therefore \angle 1 = 72^{\circ} $.

1. Believe it or not,the two surveys have similar results.
2. She helps me with my homework and she always gives her seat on the bus to someone in need.
3. Children like the Spring Festival because they can wear new clothes and get lucky money from the elders.
4. During the Spring Festival,children often get red packets with money in it.
5. To protect children’s eyes,they should not play online games for more than one hour a week.

答案： 1. surveys 2. in need 3. lucky money 4. red packets 5. online

1. Tom D thirty yuan on these two books and Lily’s books D her fifty yuan.
A.spends；spend
B.pays；cost
C.pays；spend
D.spends；cost

答案： D