1. How to recognize congruent figures and their corresponding parts. Chapter 4.1GeometryStandard/Goal: 4.1

2. 1. Check and discuss assignment from yesterday. 2. Read, write, and discuss how to recognize congruent figures and their corresponding parts. 3. Work on assignment.

3. Congruent Polygons have congruent corresponding parts their matching sides and angles. Matching vertices are corresponding vertices. When you name congruent polygons, always list corresponding vertices in the same order. A C B E GF

4. If two angles of one triangle are congruent to two angles of another triangle, Then the third angles are congruent.

5. List the corresponding sides in the same order. List the corresponding vertices in the same order. ABC QTJ. List the congruent corresponding parts. Angles:  A   Q  B   T  C   J Sides: ABQTBCTJACQJ 

6. XYZ KLM, m  Y = 67, and m  M = 48. Find m  X. Use the Triangle Angle-Sum Theorem and the definition of congruent polygons to find m  X. m  X = 65Subtract 115 from each side. m  X + m  Y + m  Z =180Triangle Angle-Sum Theorem m  Z = m  M Corresponding angles of congruent triangles that are congruent m  Z = 48Substitute 48 for m  M. m  X + 67 + 48= 180Substitute. m  X + 115 = 180Simplify.

7. Can you conclude that ABC CDE in the figure below? List corresponding vertices in the same order. If ABC CDE, then  BAC  DCE. The diagram above shows  BAC  DEC, not  DCE. Corresponding angles are not necessarily congruent, therefore you cannot conclude that ABC CDE.

8. Show how you can conclude that CNG DNG. List statements and reasons. Congruent triangles have three congruent corresponding sides and three congruent corresponding angles. Examine the diagram, and list the congruent corresponding parts for CNG and DNG. a. CG DG Given b. CN DN Given c. GN GN Reflexive Property of Congruence d.  C  D Given e.  CNG  DNG Right angles are congruent. f.  CGN  DGN If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent. (Theorem 4-1.) g. CNG DNG Definition of triangles

9. Kennedy, D., Charles, R., Hall, B., Bass, L., Johnson, A. (2009) Geometry Prentice Hall Mathematics. Power Point made by: Robert Orloski Jerome High School.