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High school geometry

Course: High school geometry > Unit 1

Lesson 1: Intro to Euclidean geometry
Math
High school geometry
Performing transformations
Intro to Euclidean geometry
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Getting ready for performing transformations

Google Classroom
Identifying points, identifying number opposites, estimating angles, and calculating distance help prepare us to perform transformations.
All of math builds on earlier concepts, and geometry is no exception!
Let's refresh some of the earlier concepts that will come in handy as we explore transformations. We'll have links for more practice for any concept in case you would like additional review. Then we'll look ahead to how the idea will help us with transformations.

Identifying and plotting points on the coordinate plane

Practice

Problem 1.1
Use the following coordinate plane to write the ordered pair for each point.
PointOrdered pair
A(
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
,
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
)
B(
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
,
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
)
C(
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
,
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
)

For more practice, go to Points on the coordinate plane.

Where will we use this?

There are many ways to transform figures: using a coordinate plane, using a compass and straightedge, folding and layering translucent paper, or using geometry software. Identifying and plotting points will be a building block of transforming on the coordinate plane.
Here are a few of the exercises that build off of the coordinate plane:

Identifying the opposite of a number

Practice

Problem 2
Which point represents the opposite of −3 on the number line?
A number line counting from negative 7 to positive 7. Point A is at negative 7. Point B is at negative 2. Point C is at positive 3. Point D is at positive 4. Point E is at positive 7.
Choose 1 answer:

For more practice, go to Number opposites.

Where will we use this?

Reflections across the x-axis or y-axis involve finding the opposite of a number. Rotations by multiples of 90° about the origin also involve number opposites.
Here are a couple of the exercises that build off of number opposites:

Estimating angle measurement

Practice

Problem 3.1
Look at the angle shown below.
An angle is given. The angle is similar to the hands of a clock at eight a.m. or eight p.m. The measure of the angle is the longer rotation between the rays.
Estimate the measure of the angle.
Choose 1 answer:

For more practice, go to Estimate angle measures.

Where will we use this?

We will take our estimations a step further, using positive and negative angle measures to indicate the direction and amount of a rotation. We use this skill in the Rotate points exercise.
Be careful: estimating angle measures only makes sense when our figure is to scale. It is just as important to know when not to estimate as to know when we should.

Calculating distance with the Pythagorean theorem

Practice

Problem 4
What is the distance between the following points?
A coordinate plane with 2 points on it. The x- and y- axes scale by one. The first point is 6 spaces to the left of the origin and up four spaces. The second point is 5 spaces left of the origin and down 4 spaces.
Choose 1 answer:

For more practice, go to Distance between two points.

Where will we use this?

Although translations, reflections, and rotations all preserve distance, dilation generally changes the distance between a point and the center of dilation. We will determine scale factor by comparing distances, and we will create figures with proportional side lengths to the pre-image.
Here are a couple of the exercises that build off of calculating distance:

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