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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

Problem 1
Find the value of x in the triangle shown below.
A triangle with angles twenty degrees, seventy-four degrees, and x degrees.
x, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
degree

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

Problem 2.1
What is the area of the rectangle?
A rectangle with the width of five centimeters and a length of seven centimeters.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
square centimeters

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

Problem 3
Below are two parallel lines with a third line intersecting them.
Label each angle with its angle measure.
You may use each label as many or as few times as you need.
Click each dot on the image to select an answer.

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:

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