Chapter 4 Final Review

1. Congruence Chapter 4 Final Review By: Eddie Pyne & Sven Patterson

2. 4.1 - Coordinates and Distance Origin: Center of a coordinate system Coordinates: The numbers assigned to a point in a coordinate system 1D Coordinate System: A system to order numbers in a line; like a ruler 2D Coordinate System: System to locate points in a plane Axis: The perpendicular lines in a 2D coordinate system X-Axis: The horizontal axis Y-Axis: The vertical axis Quadrants: The regions which the axis separate the plane; there are 4 Distance Formula:

3. 4.2 - Polygons and Congruence Polygon: A connected set of at least three line segments in the same plane such that each segment intersects exactly two others, one at each midpoint Congruent: Polygons with equal size and shape Correspondence: Having equivalence between two parts of a figure Congruence: Establishing the correspondence between two parts of a figure Definition of Congruent Triangles: Two triangles are congruent iff there is a correspondence between their vertices such that all of their corresponding sides and angles are equal Corollary: Two triangles congruent to a third are congruent to each other Lab: We discovered that it takes, at minimum, three equal corresponding parts in triangles, including at least one side, to prove they are congruent.

4. Examples

5. 4.3 - ASA and SAS Congruence Angle-Side-Angle Postulate (ASA): If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent Side-Angle-Side Postulate (SAS): If two sides and the included angle of one triangle are equal to two angels and the included side of another triangle, the triangles are congruent

6. 4.4 - Congruence Proofs Definition of Corresponding Parts (CPCTE): Corresponding parts of congruent triangles are equal This section of Chapter 4 was mostly about proving triangles congruent. Along with this section, we had two proof packets that we did for homework. Links to proof packets that were homework: Proof Packet 1 Proof Packet 2

7. 4.5 - Isosceles and Equilateral Triangles Definitions of Triangles (Based on Sides): Scalene: iff it has no equal sides Isosceles: iff it has at least two equal sides Equilateral: iff all of its sides are equal Definitions of Triangles (Based on Angles): Obtuse: iff it has an obtuse angle Right: iff it has a right angle Acute: iff all of its angles are acute Equiangular: iff all of its angles are equal

8. 4.5 - Isosceles and Equilateral Triangles (Continued) Theorems: Isosceles Triangle Theorem (ITT): If two sides of a triangle are equal, the angles opposite them are equal. (And its corollary) An equilateral triangle is equiangular. (And its corollary)

9. 4.6 - SSS Congruence Side-Side-Side Theorem (SSS): If the three sides of one triangle are equal to the three sides of another triangle, the triangles are congruent.

10. 4.7 - Constructions The 5 main constructions: Bisecting a line segment Bisecting an angle Copying a line segment Copying an angle Copying a triangle

11. Things to Remember • Distance Formula - • Congruence (ASA, SAS, SSS) • Mrs. Liedell doesn't swear (No ASS Congruence) • Corresponding Parts of Congruent Triangle are Equal (CPCTE) • Isosceles Triangle Theorem (Converse) (ITT)