Holt McDougal Geometry Symmetry Warm Up Identify each transformation. 3. A(3, –4), B(5, 1),...
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Transcript of Holt McDougal Geometry Symmetry Warm Up Identify each transformation. 3. A(3, –4), B(5, 1),...
![Page 1: Holt McDougal Geometry Symmetry Warm Up Identify each transformation. 3. A(3, –4), B(5, 1), C(–4, 0); 180° 1. 2. Rotate ∆ABC with the given vertices by.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551bcbe9550346b4588b518d/html5/thumbnails/1.jpg)
Holt McDougal Geometry
Symmetry
Warm UpIdentify each transformation.
3. A(3, –4), B(5, 1), C(–4, 0); 180°
1. 2.
Rotate ∆ABC with the given vertices by the given angle.
4. A(1, –5), B(7, –1), C(3, 6); 90°
![Page 2: Holt McDougal Geometry Symmetry Warm Up Identify each transformation. 3. A(3, –4), B(5, 1), C(–4, 0); 180° 1. 2. Rotate ∆ABC with the given vertices by.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551bcbe9550346b4588b518d/html5/thumbnails/2.jpg)
Holt McDougal Geometry
Symmetry
Diatoms are microscopic algae that are found in aquatic environments. Scientists use a system that was developed in the 1970s to classify diatoms based on their symmetry.
A figure has symmetry if there is a transformation of the figure such that the image coincides with the preimage.
![Page 3: Holt McDougal Geometry Symmetry Warm Up Identify each transformation. 3. A(3, –4), B(5, 1), C(–4, 0); 180° 1. 2. Rotate ∆ABC with the given vertices by.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551bcbe9550346b4588b518d/html5/thumbnails/3.jpg)
Holt McDougal Geometry
Symmetry
![Page 4: Holt McDougal Geometry Symmetry Warm Up Identify each transformation. 3. A(3, –4), B(5, 1), C(–4, 0); 180° 1. 2. Rotate ∆ABC with the given vertices by.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551bcbe9550346b4588b518d/html5/thumbnails/4.jpg)
Holt McDougal Geometry
Symmetry
Example 1A: Identifying line of symmetry
Tell whether the figure has line symmetry. If so, copy the shape and draw all lines of symmetry.
![Page 5: Holt McDougal Geometry Symmetry Warm Up Identify each transformation. 3. A(3, –4), B(5, 1), C(–4, 0); 180° 1. 2. Rotate ∆ABC with the given vertices by.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551bcbe9550346b4588b518d/html5/thumbnails/5.jpg)
Holt McDougal Geometry
Symmetry
Example 1B: Identifying line of symmetry
Tell whether the figure has line symmetry. If so, copy the shape and draw all lines of symmetry.
![Page 6: Holt McDougal Geometry Symmetry Warm Up Identify each transformation. 3. A(3, –4), B(5, 1), C(–4, 0); 180° 1. 2. Rotate ∆ABC with the given vertices by.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551bcbe9550346b4588b518d/html5/thumbnails/6.jpg)
Holt McDougal Geometry
Symmetry
Example 1C: Identifying line of symmetry
Tell whether the figure has line symmetry. If so, copy the shape and draw all lines of symmetry.
![Page 7: Holt McDougal Geometry Symmetry Warm Up Identify each transformation. 3. A(3, –4), B(5, 1), C(–4, 0); 180° 1. 2. Rotate ∆ABC with the given vertices by.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551bcbe9550346b4588b518d/html5/thumbnails/7.jpg)
Holt McDougal Geometry
Symmetry
Tell whether each figure has line symmetry. If so, copy the shape and draw all lines of symmetry.
Check It Out! Example 1
a.
b.
c.
![Page 8: Holt McDougal Geometry Symmetry Warm Up Identify each transformation. 3. A(3, –4), B(5, 1), C(–4, 0); 180° 1. 2. Rotate ∆ABC with the given vertices by.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551bcbe9550346b4588b518d/html5/thumbnails/8.jpg)
Holt McDougal Geometry
Symmetry
![Page 9: Holt McDougal Geometry Symmetry Warm Up Identify each transformation. 3. A(3, –4), B(5, 1), C(–4, 0); 180° 1. 2. Rotate ∆ABC with the given vertices by.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551bcbe9550346b4588b518d/html5/thumbnails/9.jpg)
Holt McDougal Geometry
Symmetry
The angle of rotational symmetry is the smallest angle through which a figure can be rotated to coincide with itself. The number of times the figure coincides with itself as it rotates through 360° is called the order of the rotational symmetry.
![Page 10: Holt McDougal Geometry Symmetry Warm Up Identify each transformation. 3. A(3, –4), B(5, 1), C(–4, 0); 180° 1. 2. Rotate ∆ABC with the given vertices by.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551bcbe9550346b4588b518d/html5/thumbnails/10.jpg)
Holt McDougal Geometry
Symmetry
Example 2: Identifying Rotational Symmetry
Tell whether each figure has rotational symmetry. If so, give the angle of rotational symmetry and the order of the symmetry.
A. B.
C.
![Page 11: Holt McDougal Geometry Symmetry Warm Up Identify each transformation. 3. A(3, –4), B(5, 1), C(–4, 0); 180° 1. 2. Rotate ∆ABC with the given vertices by.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551bcbe9550346b4588b518d/html5/thumbnails/11.jpg)
Holt McDougal Geometry
Symmetry
Check It Out! Example 2
Tell whether each figure has rotational symmetry. If so, give the angle of rotational symmetry and the order of the symmetry.
a. b. c.
![Page 12: Holt McDougal Geometry Symmetry Warm Up Identify each transformation. 3. A(3, –4), B(5, 1), C(–4, 0); 180° 1. 2. Rotate ∆ABC with the given vertices by.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551bcbe9550346b4588b518d/html5/thumbnails/12.jpg)
Holt McDougal Geometry
Symmetry
Example 3A: Design Application
Describe the symmetry of each icon. Copy each shape and draw any lines of symmetry. If there is rotational symmetry, give the angle and order.
![Page 13: Holt McDougal Geometry Symmetry Warm Up Identify each transformation. 3. A(3, –4), B(5, 1), C(–4, 0); 180° 1. 2. Rotate ∆ABC with the given vertices by.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551bcbe9550346b4588b518d/html5/thumbnails/13.jpg)
Holt McDougal Geometry
Symmetry
Example 3B: Design Application
Describe the symmetry of each icon. Copy each shape and draw any lines of symmetry. If there is rotational symmetry, give the angle and order.
![Page 14: Holt McDougal Geometry Symmetry Warm Up Identify each transformation. 3. A(3, –4), B(5, 1), C(–4, 0); 180° 1. 2. Rotate ∆ABC with the given vertices by.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551bcbe9550346b4588b518d/html5/thumbnails/14.jpg)
Holt McDougal Geometry
Symmetry
Check It Out! Example 3
Describe the symmetry of each diatom. Copy the shape and draw any lines of symmetry. If there is rotational symmetry, give the angle and order.
a. b.
![Page 15: Holt McDougal Geometry Symmetry Warm Up Identify each transformation. 3. A(3, –4), B(5, 1), C(–4, 0); 180° 1. 2. Rotate ∆ABC with the given vertices by.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551bcbe9550346b4588b518d/html5/thumbnails/15.jpg)
Holt McDougal Geometry
Symmetry
A three-dimensional figure has plane symmetry if a plane can divide the figure into two congruent reflected halves.
Plane symmetry
![Page 16: Holt McDougal Geometry Symmetry Warm Up Identify each transformation. 3. A(3, –4), B(5, 1), C(–4, 0); 180° 1. 2. Rotate ∆ABC with the given vertices by.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551bcbe9550346b4588b518d/html5/thumbnails/16.jpg)
Holt McDougal Geometry
Symmetry
A three-dimensional figure has symmetry about an axis if there is a line about which the figure can be rotated (by an angle greater than 0° and less than 360°) so that the image coincides with the preimage.
Symmetry about an axis
![Page 17: Holt McDougal Geometry Symmetry Warm Up Identify each transformation. 3. A(3, –4), B(5, 1), C(–4, 0); 180° 1. 2. Rotate ∆ABC with the given vertices by.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551bcbe9550346b4588b518d/html5/thumbnails/17.jpg)
Holt McDougal Geometry
Symmetry
Example 4A: Identifying Symmetry in Three Dimensions
Tell whether the figure has plane symmetry, symmetry about an axis, or neither.
![Page 18: Holt McDougal Geometry Symmetry Warm Up Identify each transformation. 3. A(3, –4), B(5, 1), C(–4, 0); 180° 1. 2. Rotate ∆ABC with the given vertices by.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551bcbe9550346b4588b518d/html5/thumbnails/18.jpg)
Holt McDougal Geometry
Symmetry
Example 4B: Identifying Symmetry in Three Dimensions
Tell whether the figure has plane symmetry, symmetry about an axis, or neither.
![Page 19: Holt McDougal Geometry Symmetry Warm Up Identify each transformation. 3. A(3, –4), B(5, 1), C(–4, 0); 180° 1. 2. Rotate ∆ABC with the given vertices by.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551bcbe9550346b4588b518d/html5/thumbnails/19.jpg)
Holt McDougal Geometry
Symmetry
Check It Out! Example 4
Tell whether each figure has plane symmetry, symmetry about an axis, or no symmetry.
a. cone b. pyramid
![Page 20: Holt McDougal Geometry Symmetry Warm Up Identify each transformation. 3. A(3, –4), B(5, 1), C(–4, 0); 180° 1. 2. Rotate ∆ABC with the given vertices by.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551bcbe9550346b4588b518d/html5/thumbnails/20.jpg)
Holt McDougal Geometry
Symmetry
Lesson Quiz: Part I
Describe the symmetry of each figure. Draw any lines of symmetry. Give the angle and the order of any rotational symmetry.
1.
2.
![Page 21: Holt McDougal Geometry Symmetry Warm Up Identify each transformation. 3. A(3, –4), B(5, 1), C(–4, 0); 180° 1. 2. Rotate ∆ABC with the given vertices by.](https://reader035.fdocuments.net/reader035/viewer/2022062621/551bcbe9550346b4588b518d/html5/thumbnails/21.jpg)
Holt McDougal Geometry
Symmetry
Lesson Quiz: Part II
Tell whether each figure has plane symmetry, symmetry about an axis, or neither.
3.
4.