In the Diagram Below Abc Is Similar to Art

May 05, 2022 Post a Comment

1. A two-dimensional cross section is taken of a three-dimensional object. If this cross section is a triangle, what can not be the three dimensional object?

(1) cone
(2) cylinder
(3) pyramid
(4) rectangular prism

2. The image of $\triangle DEF$ is $\triangle D'E'F'$ . Under which transformation will the triangles not exist congruent?

(1) a reflection through the origin
(2) a reflection over the line $y = x$
(3) a dilation with a calibration gene of $1$ centered at ( $2,3$ )
(4) a dilation with a scale factor of $\dfrac{3}{2}$ centered at the origin

3. The vertices of foursquare $RSTV$ have coordinates $R(-1,5), S(-3,1), T(-7,3),$ and $V(-5,7)$ . What is the perimeter of $RSTV$ ?

(1) $\sqrt{20}$
(2) $\sqrt{40}$
(3) $4\sqrt{20}$
(four) $4\sqrt{40}$

four. In the diagram below of circle $O$ , chord $\overline{CD}$ is parallel to diameter $\overline{AOB}$ and $m\widehat{CD} = 130$

What is $m\widehat{AC}$ ?

(1) $25$
(2) $50$
(3) $65$
(4) $115$

5. In the diagram beneath, $\overline{AD}$ intersects $\overline{BE}$ at $C$ , and $\overline{AB} \| \overline{DE}$ .

If $CD = 6.6$ cm, $DE = 3.4$ cm, $CE = 4.2$ cm, and $BC = 5.25$ cm, what is the length of $\overline{AC}$ , to the nearest hundredth of a centimeter?

(one) $2.70$
(2) $3.34$
(iii) $5.28$
(4) $8.25$

6. As shown in the graph below, the quadrilateral is a rectangle.

Which transformation would not map the rectangle onto itself?

(ane) a reflection over the $x$ -centrality
(2) a reflection over the line $x = 4$
(3) a rotation of $180^{\circ}$ almost the origin
(4) a rotation of $180^{\circ}$ about the point ( $4,0$ )

seven. In the diagram below, triangle $ACD$ has points $B$ and $E$ on sides $\overline{AC}$ and $\overline{AD}$ , respectively, such that $\overline{BE} \| \overline{CD}, AB = 1, BC = 3.5,$ and $AD = 18$ .

What is the length of $\overline{AE}$ , to the nearest tenth?

(1) $14.0$
(ii) $5.1$
(three) $3.3$
(iv) $4.0$

eight. In the diagram below of parallelogram $ROCK, m\angle C$ is $70^{\circ}$ and $m\angle ROS$ is $65^{\circ}$ .

What is $m\angle KSO$ ?

(one) $45^{\circ}$
(2) $110^{\circ}$
(iii) $115^{\circ}$
(4) $135^{\circ}$

9. In the diagram beneath, $\angle GRS \cong \angle ART, GR = 36, SR = 45, AR = 15,$ and $RT = 18$ .

Which triangle similarity statement is correct?

(1) $\triangle GRS \sim \triangle ART$ by AA
(two) $\triangle GRS \sim \triangle ART$ by SAS
(3) $\triangle GRS \sim \triangle ART$ by SS
(4) $\triangle GRS$ is not similar to $\triangle ART$

10. The line represented past the equation $4y = 3x + 7$ is transformed by a dilation centered at the origin. Which linear equation could stand for its prototype?

(ane) $14.0$
(2) $5.1$
(3) $3.3$
(4) $4.0$

11. Given $\triangle ABC$ with $m\angle B = 62^{\circ}$ and side $\overline{AC}$ extended to $D$ equally shown below.

Which value of $x$ makes $\overline{AB} \cong \overline{CB}$ ?

(1) $59^{\circ}$
(2) $62^{\circ}$
(3) $118^{\circ}$
(4) $121^{\circ}$

12. In the diagram shown below, $\overline{PA}$ is tangent to circumvolve $T$ at $A$ , and secant $\overline{PBC}$ is drawn where point $B$ is on circle $T$ .

If $PB = 3$ and $BC = 15$ , what is the length of $\overline{PA}$ ?

(1) $3\sqrt{5}$
(2) $3\sqrt{6}$
(3) $3$
(iv) $9$

13. A rectangle whose length and width are $10$ and $6$ , respectively, is shown below. The rectangle is continuously rotated around a directly line to grade an object whose volume is $150\pi$ .

Which line could the rectangle be rotated around?

(i) a long side
(2) a short side
(iii) the vertical line of symmetry
(four) the horizontal line of symmetry

14. If $ABCD$ is a parallelogram, which statement would prove that $ABCD$ is a rhomb?

(ane) $\angle ABC \cong \angle CDA$
(2) $\overline{AC} \cong \overline{BD}$
(3) $\overline{AC} \perp \overline{BD}$
(4) $\overline{AB} \perp \overline{CD}$

15. To build a handicapped-access ramp, the building lawmaking states that for every $1$ inch of vertical ascension in meridian, the ramp must extend out $12$ inches horizontally, every bit shown in the diagram below.

What is the angle of inclination, $x$ , of this ramp, to the nearest hundredth of a degree?

(1) $4.76$
(2) $4.78$
(3) $85.22$
(4) $85.24$

xvi. In the diagram below of $\triangle ABC, D, E,$ and $F$ are the midpoints of $\overline{AB}, \overline{BC},$ and $\overline{CA}$ , respectively.

What is the ratio of the area of $\triangle CFE$ to the area of $\triangle CAB$ ?

(1) $1:1$
(two) $1:2$
(3) $1:3$
(4) $1:4$

17. The coordinates of the endpoints of $\overline{AB}$ are $A(-8, -2)$ and $B(16, 6)$ . Bespeak $P$ is on $\overline{AB}$ . What are the coordinates of bespeak $P$ , such that $AP:PB$ is $3:5$ ?

(1) ( $1, 1$ )
(2) ( $7, 3$ )
(iii) ( $9.6, 3.6$ )
(4) ( $6.4, 2.8$ )

18. Kirstie is testing values that would make triangle $KLM$ a correct triangle when $\overline{LN}$ is an altitude, and $KM = 16$ equally shown below.

Which lengths would make triangle KLM a right triangle?

(1) $LM = 13$ and $KN = 6$
(2) $LM = 12$ and $KN = 9$
(3) $KL = 11$ and $KN = 7$
(4) $LN = 8$ and $NM = 10$

19. In right triangle $ABC, m\angle A = 32^{\circ}, m\angle B = 90^{\circ},$ and $AC = 6.2$ cm. What is the length of $\overline{BC}$ , to the nearest 10th of a centimeter?

(1) $3.3$
(2) $3.9$
(3) $5.3$
(four) $11.7$

20. The 2010 U.S. Census populations and population densities are shown in the table below.

Based on the table above, which list has usa' areas, in square miles, in order from largest to smallest?

(one) Illinois, Florida, New York, Pennsylvania
(two) New York, Florida, Illinois, Pennsylvania
(three) New York, Florida, Pennsylvania, Illinois
(4) Pennsylvania, New York, Florida, Illinois

21. In a correct triangle, $sin (40 - x)^{\circ} = cos (3x)^{\circ}$ . What is the value of $x$ ?