1. 2-5: Reasoning in Algebra and Geometry

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

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

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

5. Properties of Congruence
Property
Example
Reflexive
Symmetric
Transitive

6. Classwork: Worksheet

7. Section 3-1 Lines & Angles

8. 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

9. 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

10. 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

11. 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

12. 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

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