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Contact [7]
3 years ago
10

Regular hexagon ABCDEF rotates 240° counterclockwise about its center to produce hexagon A'B'C'D'E'F'. Which points will A' and

B' coincide with in the preimage?
a) A' coincides with D and B' coincides with E
b) A' coincides with E and B' coincides with F
c) A' coincides with E and B' coincides with D
d) A' coincides with D and B' coincides with C
e) A' coincides with F and B' coincides with E
Mathematics
1 answer:
Mrac [35]3 years ago
5 0

To answer this specific problem, the points that A’ and B’ will coincide with in the preimage is “A' coincides with E and B' coincides with D.” The correct answer between all the choices given is the third choice or letter C. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.

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Given: ABCD is a trapezoid, AB=CD, MN is a midsegment, MN=30, BC=17, AB=26 Find: m∠A, m∠B, m∠C, and m∠D
enyata [817]

Answer:

The measures of angle ∠A, ∠B, ∠C, and ∠D are 60, 120, 120 and 60 degree respectively.

Step-by-step explanation:

Given information:AB=CD, MN is a midsegment, MN=30, BC=17, AB=26

Since two opposites sides are equal, therefore we can say that two no parallel sides are equal.

The length of midsegment is average of length of parallel lines.

MN=\frac{AD+BC}{2}

30=\frac{AD+17}{2}

60=AD+17

43=AD

Draw perpendiculars on AD from B and C. Let angle A be θ. D

AD=AE+EF+FD

Since ABCD is an isosceles trapezoid, therefore AE=FD and EF=BC

AD=AE+EF+AE

43=2(AE)+17

26=2(AE)

13=AE

\cos\theta=\frac{base}{hypotenuse}

\cos\theta=\frac{AE}{AB}

\cos\theta=\frac{13}{26}

\cos\theta=\frac{1}{2}

\theta=\cos^{-1}\frac{1}{2}

\theta=60

Since ABCD is an isosceles trapezoid, therefore angles A and D are same. Angle B and C are same.

\angle A=\angle D=60^{\circ}

The sum of two consecutive angles of a trapezoid is 180 degree by consecutive interior angle theorem.

\angle A+\angle B=180^{\circ}

60^{\circ}+\angle B=180^{\circ}

\angle B=120^{\circ}

\angle B=\angle C=120^{\circ}

Therefore measures of angle ∠A, ∠B, ∠C, and ∠D are 60, 120, 120 and 60 degree respectively.

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