# Lesson 1 How Do You Know That? Develop Understanding

It is said that a picture is worth a thousand words. Mathematical symbols can be just as important when communicating about geometric diagrams. Decide which of the symbolic statements are correct based on what is given in the diagram. Justify your answers.

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#### a.

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#### d.

Create a diagram based on the given symbolic statement. Be sure enough information is provided in the diagram to validate each statement.

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There are four “ways of knowing” that were discussed as part of today’s lesson. They are “knowing” based on: Authority, Examples, Diagrams, and Logical Reasoning.

Consider each of the scenarios below and identify which “way of knowing” best describes what is happening.

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Every time I have drawn a ray with its endpoint on a line and measure the two angles formed with a protractor, they add up to

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Knowing based on authority

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Knowing based on examples

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Knowing based on diagrams

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Knowing based on logical reasoning

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You know triangles that have a right angle are classified as right triangles. And you know the sides of a right triangle have a relationship described by the Pythagorean theorem. So you have concluded that when you have a triangle with a right angle you can use the Pythagorean theorem to find missing sides.

#### A.

Knowing based on authority

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Knowing based on examples

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Knowing based on diagrams

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Knowing based on logical reasoning

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I know supplementary means the two angles add up to

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Knowing based on authority

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Knowing based on examples

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Knowing based on diagrams

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Knowing based on logical reasoning

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We tore off the corners of a triangle and placed them together to have a straight line. Since we had everyone in our class do it we know the angles of a triangle will add up to

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Knowing based on authority

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Knowing based on examples

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Knowing based on diagrams

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Knowing based on logical reasoning

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I know the Pythagorean Theorem only works for right triangles because I read it in a book. It said it is a relationship to only be used with right triangles.

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Knowing based on authority

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Knowing based on examples

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Knowing based on diagrams

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Knowing based on logical reasoning

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I know you can always turn a quadrilateral into two triangles because of the way they look. Just draw a picture of any quadrilateral and then connect opposite corners and you will have two triangles. It works because of the drawing, try it.

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Knowing based on authority

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Knowing based on examples

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Knowing based on diagrams

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Knowing based on logical reasoning

If two angles share a vertex and together they make a straight angle, then the two angles are called a **linear pair**. (Below are 3 examples of **linear pairs**.)

Examples of linear pairs in real life:

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Draw at least

For

Find the measure of the missing angle.

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Linear pairs could be defined as being **supplementary angles** because they always add up to

Find the supplement of the given angle. Then draw the two angles as linear pairs. Label each angle with its measure.