Exploring Segment and Angle Addition Postulate Proofs

Miss Kers introduces the angle and segment addition postulates, demonstrating their use in geometric proofs. The video covers three examples: proving segment equality using the segment addition postulate, converting congruence to equality, and using the angle addition postulate. Each example follows a structured approach involving reading the problem, marking diagrams, and applying postulates and properties like substitution and subtraction. The video concludes with a summary of the proof process.

What does the Segment Addition Postulate state?

• If two angles are adjacent, their measures are equal.

• If a point is between two other points, the sum of the segments equals the whole segment.

• Two segments are congruent if they have the same length.

• The sum of the angles in a triangle is 180 degrees.

In the Segment Addition Postulate, if AB = 5 and BC = 7, what is AC?

• 1

• 35

• 2

• 12

What is the first step in solving a proof using the Segment Addition Postulate?

• Draw the diagram.

• Write the given information.

• Find the midpoint.

• Use the Subtraction Property.

In Example 1, what property is used to rewrite the first equation?

• Multiplication Property

• Substitution Property

• Addition Property

• Division Property

In Example 2, why do we change from congruence to equality?

• Because congruence is not allowed in proofs.

• To simplify the diagram.

• To make the segments longer.

• Because the Segment Addition Postulate uses measures, not congruence.

What is the final step in proving XZ equals YZ in Example 2?

• Change equality back to congruence.

• Use the Subtraction Property.

• Draw a new diagram.

• Find the midpoint.

In Example 3, what is the Angle Addition Postulate used for?

• To prove two segments are congruent.

• To find the midpoint of a segment.

• To calculate the area of a triangle.

• To express a large angle as the sum of two smaller angles.

What property is used to prove that the measure of angle GBC equals the measure of angle HEF?

• Division Property of Equality

• Multiplication Property of Equality

• Addition Property of Equality

• Subtraction Property of Equality

Why do we need to change measures back to congruence in the final step of Example 3?

• To simplify the diagram.

• To make the angles larger.

• Because the proof requires congruence, not just equality.

• To find the midpoint.

What common steps are followed in proofs using the Segment or Angle Addition Postulate?

• Use the multiplication property, division property, and draw a new diagram.

• Draw a diagram, find the midpoint, and use the addition property.

• Find the area, use the subtraction property, and change to congruence.

• Use the postulate, substitution, and sometimes the subtraction property.