Solve each equation. 1.x + 6 = 252.x = x = 5404.x + 10 = 2x 5.For the triangle at the right, use the Triangle Angle-Sum Theorem to find the value of y. (For help, go to Algebra Review, page 30.) GEOMETRY LESSON 4-1 Congruent Figures 4-1 Check Skills You’ll Need x = 19 x = 13 x = 108 x = 10 y = 50

Congruent Figures GEOMETRY LESSON Geometric figures are congruent if they are the same size and shape. Corresponding angles and corresponding sides are in the same position in polygons with an equal number of sides. Two polygons are congruent polygons if and only if their corresponding sides and corresponding angles are congruent.

Congruent Figures GEOMETRY LESSON In a congruence statement, the order of the vertices indicates the corresponding parts. When you write a statement such as ABC  DEF, you are also stating which parts are congruent. Helpful Hint

List the corresponding sides in the same order. List the corresponding vertices in the same order. Congruent Figures GEOMETRY LESSON 4-1 ABC QTJ. List the congruent corresponding parts. Angles:  A  Q  B  T  C  J Sides: ABQTBCTJACQJ 4-1 Quick Check Naming Congruent Parts

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. Congruent Figures GEOMETRY LESSON 4-1 m  X + m  Y + m  Z=180Triangle Angle-Sum Theorem m  Z = m  MCorresponding angles of congruent triangles that are congruent m  Z = 48Substitute 48 for m  M. m  X = 180Substitute. m  X = 180Simplify. 4-1 Quick Check Using Congruent Polygons

Can you conclude that ABC CDE in the figure below? List corresponding vertices in the same order. Congruent Figures GEOMETRY LESSON 4-1 If ABC CDE, then  BAC  DCE. The diagram above shows  BAC  DEC, not  DCE. 4-1 Corresponding angles are not necessarily congruent, therefore you cannot conclude that ABC CDE. Quick Check Finding Congruent Triangles

Congruent Figures GEOMETRY LESSON Theorem 4-1

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. Congruent Figures GEOMETRY LESSON 4-1 a. CG DGGiven b. CN DNGiven c. GN GNReflexive Property of Congruence d.  C  DGiven e.  CNG  DNG Right angles are congruent. f.  CGN  DGN Third Angles Theorem g. CNG DNGDefinition of  triangles 4-1 Quick Check Proving Triangles Congruent

In Exercises 1 and 2, quadrilateral WASH quadrilateral NOTE. 1.List the congruent corresponding parts. 2.m  O = m  T = 90 and m  H = 36. Find m  N. 3.Write a statement of triangle congruence. 4.Write a statement of triangle congruence. 5.Explain your reasoning in Exercise 4 above. 144 Congruent Figures GEOMETRY LESSON 4-1 Sample: Two pairs of corresponding sides and two pairs of corresponding angles are given.  C  A because all right angles are congruent. BD BD by the Reflexive Property of. ABD CDB by the definition of congruent triangles. Sample: DFH ZPR Sample: ABD CDB 4-1 WA NO, AS OT, SH TE, WH NE;  W  N,  A  O,  S  T,  H  E