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## High school geometry

### Unit 2: Lesson 1

Rigid transformations overview- Getting ready for transformation properties
- Finding measures using rigid transformations
- Find measures using rigid transformations
- Rigid transformations: preserved properties
- Rigid transformations: preserved properties
- Mapping shapes
- Mapping shapes

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# Getting ready for transformation properties

Finding missing triangle angle measures, area and perimeter, and angle measures on transversals help prepare us to learn the properties of transformations.

Let's refresh some of the earlier concepts that will come in handy as we dig deeper into transformations. Then we'll look ahead to how the idea will help us with transformation properties.

## Finding missing angle measures in triangles

### Practice

For more practice, go to Find angles in triangles.

### Where will we use this?

When we can transform one figure onto another using only rigid transformations, the two figures are congruent. We'll use congruence along with other concepts, like the fact that the interior angle measures of a triangle sum to 180, degree, to find missing measurements.

We'll use this skill in the Find measures using rigid transformations exercise.

## Finding area and perimeter

### Practice

For more practice, go to Represent rectangle measurements, Area of triangles, and Find perimeter when given side lengths.

### Where will we use this?

Rigid transformations preserve length, so we can use the measurements in a congruent figure to help us calculate the perimeter or area of another figure.

We'll use these skills in the Find measures using rigid transformations exercise.

## Using angle measures from transversals

### Practice

For more practice, go to Angle relationships with parallel lines.

### Where will we use this?

Rigid transformations preserve angle measure. The properties of angle measures on transversals will help us make sense of why translations and dilations take lines to parallel lines, but rotations and reflections usually don't.

Here are a couple of the exercises that build off of angle measures with transversals:

## Want to join the conversation?

- What are rigid transformations? And how do they work? what do we use them for irl?(7 votes)
- Rigid transformations are transformations where angles and lengths of shapes are preserved. It is like taking the same exact shape or object and moving it by reflecting it or rotating it. We use rigid transformations everyday simply by picking up and placing items somewhere else. (Like if you were to pick up a pencil and move it beside you).(1 vote)

- I'm extremely confused on problem 2.2 on finding the area of the triangle. It looks off and I got a total different answer which is 14 1/2. :((4 votes)
- For a triangle, the area is 1/2 bh. You always want the base and the height to be perpendicular to each other, so the base is 2 and the height is 5. You should never use a side that is at any angle that is not 90 degrees.(2 votes)

- why do we need this in real life(4 votes)
- bruh, like why tho, who decided i need to know this, im not gonna look at a pie and be like, Well theoretically if you look close enough then that slice is a 14 degree angle

also its definitely not a realistic career to be a mathematician(4 votes)- You use it for more than a mathematician. You can use it to cut a sandwich cmon man(1 vote)

- I do not quite understand this from the article, "The properties of angle measures on transversals will help us make sense of why translations and dilations take lines to parallel lines, but rotations and reflections usually don't."(2 votes)
- Look at when you do a dilation, or a transversal. Say a square with side AB. you will notice afterwards , in the new image of a transversal or dilation of side AB is parallel with the image that you dilated or transversed from. But.... if you do a reflection or a rotation, they will not be parallel anymore. They will cross at some point. Hope this helps.(3 votes)

- I did't get the value of x(2 votes)
- A triangles's angles add up to 180 degrees, so find a angle measure that adds up to it(3 votes)

- How does the last problem with the angles cover transformations?(2 votes)
- They say, "Then we'll look ahead to how the idea will help us with transformation properties." Preserving the angles and lengths in rigid transformations will help you later calculate the perimeter or area of a transformation. It is just going deeper into the properties and proofs of transformations.(4 votes)

- how to do rotate shapes(1 vote)
- Khan Academy has many videos, articles, and quizzes on it but here are a few:

https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-rotations/v/points-after-rotation

https://www.khanacademy.org/math/geometry-home/transformations/geo-rotations/v/rotating-about-arbitrary-point

https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-rotations/v/defining-rotation-example

https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-rotations/a/rotating-shapes

https://www.khanacademy.org/math/cc-eighth-grade-math/geometric-transformations/rotations-8th/a/rotations-review

https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-rotations/e/rotations-1

But with that aside I'll try to explain it to you. To rotate a shape around an origin (by multiples of 90), you'll need to find the coordinates of all the points. For example a triangle may have the coordinates:

A (-8, 2)

B (-8, 8)

C (-5, 2)

After you find the coordinates, you can use this technique to determine the new coordinates of all the points. If your rotating the shape 90 Degrees, the coordinate of a point will be (-y, x). When rotating a shape 90 degrees, the coordinates of a point will be (-x,-y). When rotating a shape 270 degrees, the coordinates will be (y, -x).

Note: This only works with 90 degrees, 180 degrees, and 270 degrees, when they are rotated around the origin.(5 votes)

- "The properties of angle measures on transversals will help us make sense of why translations and dilations take lines to parallel lines, but rotations and reflections usually don't."

what does this mean exactly? especially the "take lines to parallel line" part.(1 vote)- I think Sal means that when you dilate or translate a line (or figure), the original line segment(s) and the translated line segment (or corresponding segments in a figure) will be parallel to each other. This could possibly also include along the same line if you translate only in the x direction.(4 votes)

- What are rigid transformations and arrow notation?(2 votes)