It is recommended to use the [Huawen Zhong Song] font, which is more similar to the style of test papers.

I. Multiple Choice Questions (This section has 10 questions, each worth 3 points, total 30 points. Among the four options given for each question, only one meets the requirements.)

1. Among the following numbers, the smallest number is ( ※ ).

{{ select(1) }}

• $-5$
• $-2$
• $0$
• $3$

2. In $Rt\triangle ABC$, $∠C=90°$, if $∠A=26°$, then the measure of $∠B$ is ( ※ ).

{{ select(2) }}

• $26°$
• $44°$
• $54°$
• $64°$

3. As shown in Figure $1$, when the tripod of a camera is unfolded, its support structure forms multiple triangles. The mathematical basis for this design is ( ※ ).

{{ select(3) }}

• Two points determine a straight line
• Triangles have stability
• Between two points, the line segment is the shortest
• The sum of any two sides of a triangle is greater than the third side

4. Which of the following calculations is correct? ( ※ )

{{ select(4) }}

• $a^2·a^3=a^6$
• $a^3+a^4=a^7$
• $a^6÷a^2=a^3$
• $(\sqrt{2}-1)^0=1$

5. Among the following sets of three line segments, which can form a triangle? ( ※ )

{{ select(5) }}

• $2cm,3cm,4cm$
• $3cm,3cm,7cm$
• $2cm,5cm,9cm$
• $8cm,4cm,4cm$

6. The perimeter of a rectangle is $20cm$, and its length is $x\ cm$. Then the area of this rectangle is ( ※ ).

{{ select(6) }}

• $10x-x^2$
• $20x-x^2$
• $10-\frac{1}{2}x$
• $20x-2x^2$

7. As shown in Figure $2$, points $B,D,C$ lie on a straight line, $\triangle ADB\cong\triangle CDE$, with point $A$ and point $C$, point $B$ and point $E$ being corresponding vertices. Which of the following conclusions is not necessarily correct? ( ※ )

{{ select(7) }}

• $BD=DE$
• $AD⊥BC$
• $AB=CE$
• $AE=DE$

8. As shown in the figure, the triangular piece of paper $ABC$ is folded in four different ways. In which case is $CM$ the altitude of $\triangle ABC$? ( ※ )

{{ select(8) }}

• A
• B
• C
• D

9. As shown in Figure $3$, in $Rt\triangle ABC$, $∠C=90°$, with vertex $A$ as the center, draw an arc with an appropriate radius, intersecting $AC$ and $AB$ at points $M$ and $N$ respectively. Then, with $M$ and $N$ as centers, draw arcs with a radius greater than $\dfrac{1}{2}MN$. The two arcs intersect at point $P$. Draw ray $AP$ intersecting side $BC$ at point $D$. If $CD=3$ and $AB=8$, then the area of $\triangle ABD$ is ( ※ ).

{{ select(9) }}

• $3$
• $8$
• $12$
• $24$

10. As shown in Figure $4$, it is a six-pointed star $ABCDEF$, where $∠AOE=80°$, $AD$ and $BE$ intersect at $O$. Then the sum of the angles $∠A+∠B+∠C+∠D+∠E+∠F$ is ( ※ ).

{{ select(10) }}

• $240°$
• $160°$
• $100°$
• $80°$

II. Fill-in-the-Blank Questions (This section has 6 questions, each worth 3 points, total 18 points.)

11. The arithmetic square root of $9$ is {{ input(11) }}.

12. As shown in Figure $5$, $AB$ and $CD$ intersect at point $O$, $AO=CO$. To make $\triangle ADO\cong\triangle CBO$, one additional condition that needs to be added is {{ input(12) }} (Just fill in one, the symbol for angle is ∠).

13. A set of triangular plates is placed as shown in Figure $6$. $∠BAC=∠DAE=90°,∠B=45°,∠D=30°$, $F$ is the intersection of $DE$ and $BC$. If $∠DAB=30°$, then $∠DFB=$ {{ input(13) }}.

14. If the result of $-5x(x^2+a)+10x+2$ does not contain an $x$ term, then $a=$ {{ input(14) }}.

15. As shown in Figure $7$, $F$ is the centroid of $\triangle ABC$. Connect $AF$ and extend it to intersect $AC$ at point $E$. If the area of $\triangle ABF$ is $8cm^2$, then the area of quadrilateral $CDFE$ is {{ input(15) }} $cm^2$.

16. As shown in Figure $8$, in $\triangle ABC$, $AB=AC=10$ centimeters, $∠B=∠C,BC=12$ centimeters, point $D$ is the midpoint of $AB$. Point $M$ moves along segment $BC$ at a speed of $3$ centimeters per second from point $B$ to point $C$. Simultaneously, point $N$ moves along segment $AC$ from point $C$ to point $A$. When point $M$ reaches point $C$ or point $N$ reaches point $A$, the other point also stops moving. If the speed of point $N$ is $a$ centimeters per second, then

(1) After moving for $2$ seconds, $CN=$ {{ input(16-1) }} centimeters (expressed in terms of $a$);

(2) When $\triangle BDM$ is congruent to $\triangle CMN$, the value of $a$ is {{ input(16-2) }}.