2.4 Use Postulates & Diagrams 2.4 Use Postulates and Diagrams 2.4 Use Postulates & Diagrams Objectives: To understand the role of postulates in geometry To illustrate and understand postulates about lines and planes To accurately interpret geometric diagrams

Example 1 What is the length of ?

Example 1 You basically used the Segment Addition Postulate to get the length of the segment, where SA + AM = SM.

Postulates As you build a deductive system like geometry, you demonstrate that certain statements are logical consequences of other previously accepted or proven statements.

Postulates This chain of logical reasoning must begin somewhere, so every deductive system must contain some statements that are never proved. In geometry, these are called postulates.

Postulates and Theorems Postulates are statements in geometry that are so basic, they are assumed to be true without proof. Sometimes called axioms. Theorems are statements that were once conjectures but have since been proven to be true based on postulates, definitions, properties, or previously proven conjectures. Both postulates and theorems are ordinarily written in conditional form.

Eight Window Foldable Fold blank piece of paper in half length-wise. While it’s still folded, fold in half in the opposite direction.

Eight Window Foldable Now in the same direction, fold the paper in half two more times. Unfold the paper and cut along the fold lines on the right side of the paper to create eight windows.

Postulates Are Easy! On the first strip, write “Postulate.” Under that strip write the definition of postulate. Postulate

Postulates Are Easy! The other seven windows are for specific postulates. The outside strip should have a picture that illustrates the postulate that appears under the strip. Postulate

Postulates Are Easy! For example, under the second strip write: Through any two points there exists exactly one line. On the front of the second strip, draw an illustration:

Repeat Times Seven!

Example 1 State the postulate illustrated by the diagram.

Example 2 How does the diagram shown illustrate one or more postulates?

Interpreting Diagrams When you interpret a diagram, you can assume only information about size or measure if it is marked.

Interpreting Diagrams

Interpreting Diagrams

Example 3 Sketch a diagram showing TV intersecting with PQ at point W so that .

Perpendicular Figures A line is perpendicular to a plane if and only if the line intersects the plane in a point and is perpendicular to every line in the plane that intersects it at that point.

Example 4 Which of the following cannot be assumed from the diagram? A, B, and F are collinear. E, B, and D are collinear. AB  plane S

Example 4 Which of the following cannot be assumed from the diagram? CD  plane T AF intersects BC at point B.