Lesson 2-7 Proving Segment Relationships

Ohio Content Standards:

Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.

Ohio Content Standards: Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two- dimensional figures and three- dimensional objects.

Ohio Content Standards: Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof.

Postulate 2.8 Ruler Postulate

The points on any line or line segment can be paired with real numbers so that, given any two points A and B on a line, A corresponds to zero, and B corresponds to a positive real number.

Postulate 2.9 Segment Addition Postulate

If B is between A and C, then AB + BC = AC.

Postulate 2.9 Segment Addition Postulate If B is between A and C, then AB + BC = AC. If AB + BC = AC, then B is between A and C.

Prove the following. Given: PR = QS Prove: PQ = RS PQRS

Theorem 2.2 Segment Congruence

Congruence of segments is reflexive, symmetric, and transitive..

Theorem 2.2 Segment Congruence Congruence of segments is reflexive, symmetric, and transitive. Reflexive Property AB AB.

Theorem 2.2 Segment Congruence Congruence of segments is reflexive, symmetric, and transitive. Symmetric Property If AB CD, then CD AB..

Theorem 2.2 Segment Congruence Congruence of segments is reflexive, symmetric, and transitive. Transitive Property If AB CD, and CD EF, then AB EF..

Prove the following. Given:WY = YZ YZ XZ XZ WX Prove:WX WY Z WX Y 3 cm

Assignment: Pgs all, all