2-5: Reasoning in Algebra and Geometry

Properties of Equality Assume a, b and c represent real numbers. Property Definition Example Addition Subtraction Multiplication Division

Properties of Equality Assume a, b and c represent real numbers. Property Definition Example Reflexive Symmetric Transitive Substitution

Properties of Equality Assume a, b and c represent real numbers. Property Definition Example Distributive

Properties of Congruence Property Example Reflexive Symmetric Transitive

Classwork: Worksheet

Section 3-1 Lines & Angles

Key Concepts Parallel and Skew Parallel Lines – Coplanar lines that do not intersect. Symbols Skew Lines – Non coplanar lines. They are not parallel and do not intersect. are Skew Parallel Planes – Planes that do not intersect. plane ABCD // plane EFGH // means is parallel to

Ex 1. Identifying nonintersecting lines and planes. Which segments are parallel to ? Which segments are skew to ? What are two pairs of parallel planes? Which segments are parallel to plane BCGF? ABCD // EFGH DCG // ABE

Transversal Exterior 2 1 3 4 Interior 5 6 8 7 Exterior A transversal is a line that intersects two or more coplanar lines at distinct points, creating interior and exterior angles. Exterior 1 2 3 4 5 6 7 8 Interior Exterior

Angle Pairs Formed by Transversals Key Concepts Angle Pairs Formed by Transversals Alternate Interior Angles – are nonadjacent interior angles that lie on opposite sides of the transversal. 1 2 3 4 5 6 7 8 Same-side Interior Angles – are interior angles that lie on the same side of the transversal. 1 2 3 4 5 6 7 8

Angle Pairs Formed by Transversals Key Concepts Angle Pairs Formed by Transversals Corresponding Angles– lie on the same side of the transversal and are in the same position. 1 2 3 4 5 6 7 8 Alternate Exterior Angles – are nonadjacent exterior angles that lie on opposite sides of the transversal. 1 2 3 4 5 6 7 8

HW: p. 143 #’s 1-3, 17-23 when question asks for all, just put one, 25-42