The equilateral triangle has three symmetry lines.
What do we mean by rotational symmetry?
- In geometry, rotational symmetry, also recognized as radial symmetry, is the property that a shape has when it looks the same after a partial turn rotation.
- The degree of rotational symmetry of an object is the number of distinct orientations in which it appears exactly the same for each rotation.
- Certain geometric objects, such as squares rotated 90°, are partially symmetrical when rotated at certain angles; however, the only geometric objects that are fully rotationally symmetric anywhere at an angle are spheres, circles, and other spheroids.
So,
- The Geometer's Sketchpad is indeed a commercial interactive geometry software program that allows you to experiment with Euclidean geometry, algebra, calculus, and other areas of mathematics.
- In this question, we must draw an equilateral triangle in the Geometer's Sketchpad and then use the reflection tool from the transition menu to investigate and determine all possible lines of symmetry.
- Then write down their number.
- Now we'll draw the figures on the Geometer's Sketchpad.
Step 1:
- Create an equilateral triangle and label its vertices A, B, and C. Draw a perpendicular line A to BC.
- In the line, reflect the triangle.
- Display the reflected image's labels.
- This line is the line of reflection if the image maps to the original.
Step 2:
- Next, draw a line perpendicular to AC through B.
- In the line, reflect the triangle.
- Display the reflected image's labels.
- This line is the line of reflection if the image maps to the original.
Step 3:
- Draw a line C perpendicular to AB now.
- In the line, reflect the triangle.
- Display the reflected image's labels.
- This is the line of reflection if the image includes the original.
(Refer to the graphs below)
Therefore, the equilateral triangle has three symmetry lines.
Know more about rotational symmetry here:
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