1.If $\sqrt{x-1}$ is meaningful in the real number range, then the range of real number $x$ is (*).

{{ select(1) }}

• $x\ge1$
• $x>1$
• $x\le 1$
• $x<1$

2. As shown in Figure 1, in parallelogram $ABCD$, $\angle B=135^\circ$, then $\angle D=(*)^\circ$.

{{ select(2) }}

• $45°$
• $55°$
• $135°$
• $145°$

3. Among the following quadratic radicals, which one is in its simplest form? (*)

   {{ select(3) }}

• $\sqrt{12}$
• $\sqrt{0.5}$
• $\sqrt{\frac{1}{3} }$
• $\sqrt{6}$

4. Among the following sets of numbers, which can form the sides of a right triangle? (*)

   {{ select(4) }}

• $1,2,3$
• $2,3,4$
• $3,4,5$
• $4,5,6$

5. As shown in Figure 2, vertices $A$ and $B$ of $\triangle ABC$ lie on the number line, with $\angle ABC = 90°$ and $AB = BC = 1$. If point $A$ is at the origin, draw an arc with center at $A$ and radius equal to $AC$, intersecting the number line at point $D$. The number represented by point $D$ is (*)

{{ select(5) }}

• $\sqrt{2}-1$
• $\sqrt{2}$
• $\sqrt{2}+1$
• $- \sqrt{2}$

6. Given that a quadrilateral is a rectangle, to make it a square, the following conditions can be added (*)

   {{ select(6) }}

• One of the angles is 90 degrees
• The diagonals are perpendicular to each other
• The diagonals bisect each other
• The diagonals are equal

7. As shown in the figure below, an ant crawls along the surface of a cube with edge length $1$ from vertex $A$ to vertex $B$. The shortest distance it travels is (*)

{{ select(7) }}

• $\sqrt{3}$
• $1+\sqrt{3}$
• $3$
• $\sqrt{5}$

8. As shown in the figure, in the Cartesian coordinate system $xOy$, the vertex $A$ of the rhombus $OABC$ lies on the positive half of the $x$-axis. If the coordinates of point $C$ are $(3,4)$, then the coordinates of point $B$ are (*)

{{ select(8) }}

• $A(8,4)$
• $B(8,3)$
• $C(5,4)$
• $D(5,3)$

9. As shown in the figure, points $D$ and $E$ are the midpoints of segments $AB$ and $AC$ respectively, and $CD$ is the altitude of $\triangle ABC$. Given that $AB=10$ and $CD=12$, the length of $DE$ is (*)

{{ select(9) }}

• $6$
• $5$
• $\frac{13}{2}$
• $\frac{\sqrt{119}}{2}$

10. As shown in the figure, point $E$ is the midpoint of side $CD$ of rectangle $ABCD$. When $\triangle ADE$ is folded along $AE$ to form $\triangle AFE$, extending $AF$ intersects $BC$ at point $G$. Given $AB=6$ and $BC=8$, the length of $AG$ is (*)

{{ select(10) }}

• $10$
• $\frac{73}{8}$
• $9$
• $\sqrt{73}$

11. $\sqrt{3} + 2\sqrt{3} =$ {{ input(11) }}. [Use the symbol $√$ for the answer.]

12.The sum of the interior angles of a pentagon is {{ input(12) }} °

13. The Chinese knot symbolizes reunion and happiness. Xiaoyun's family has a diamond-shaped Chinese knot decoration as shown in the left image, with its schematic diagram displayed in the right image. Given that $BD=8cm$ and $AC=9cm$, the area of the diamond is ${{ input(13) }} cm^{2}$

14.In triangle ABC, with AB=√5, BC=2, and AC=1, the measure of angle ACB is {{ input(14) }} degrees

15. If the three sides of a triangle are $1$, $a$, and $2$, then $a + \sqrt{(a-3)^2} =$ {{ input(15) }}