Question
𝐴𝐵 → 𝐶𝐷 is a rotation. Which of the following statements is true?
- 𝐴𝐵 > 𝐶𝐷
- D is the image of A.
- 𝑚∠𝐴𝑂𝐶 < 𝑚∠𝐵𝑂𝐷
- 𝑚∠𝐴𝑂𝐶 ≅ 𝑚∠𝐵𝑂𝐷
Hint:
Note that figure is turned through a specific angle
The correct answer is: 𝑚∠𝐴𝑂𝐶 ≅ 𝑚∠𝐵𝑂𝐷
A rotation is a transformation that rotate every point of a figure through a specified angle and direction about a fixed point.
Since the figure is turned through a specific angle, the size remains same. Option (a) is not true
C is the image of A. Option (b) is not true
m∠𝐵𝑂𝐷 = 𝑚∠𝐴𝑂B + 𝑚∠AOD and
𝑚∠𝐴𝑂𝐶 = 𝑚∠𝐴OD + 𝑚∠DOC
We can also say that △BOA is rotated to △DOC. So, 𝑚∠𝐴𝑂B = 𝑚∠DOC
Hence, 𝑚∠𝐴𝑂𝐶 = 𝑚∠𝐴OD + 𝑚∠DOC = m∠𝐴OD + 𝑚∠AOB
So, m∠𝐵𝑂𝐷 = 𝑚∠𝐴𝑂𝐶. Option (c) is not true
Þ 𝑚∠𝐴𝑂𝐶 ≅ 𝑚∠𝐵𝑂𝐷. Option (d) is true
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