Lesson 4-2: Congruent Triangles

Lesson 4-2: Congruent Triangles Congruent Figures Congruent figures are two figures that have the same size and shape. IF two figures are congruent THEN they have the same size and shape. IF two figures have the same size and shape THEN they are congruent. Two figures are congruent IF AND ONLY IF they have the same size and shape. Lesson 4-2: Congruent Triangles

Congruent Triangles - CPCTC Two triangles are congruent IFF their corresponding parts (angles and sides) are congruent. CPCTC: Corresponding Parts of Congruent Triangles are Congruent B C A S T R = │ Vertices of the 2 triangles correspond in the same order as the triangles are named. ≡ A ↔ R; B ↔ S; C ↔ T Corresponding sides and angles of the two congruent triangles: │ = ≡ Lesson 4-2: Congruent Triangles

Lesson 4-2: Congruent Triangles  Z B A C X Y Z =  Y  B  _____ ≡ │ ≡  X │  C  ______ = Note: ∆ ZYX ∆ABC  ______ ∆ABC  ∆XYZ Lesson 4-2: Congruent Triangles

Lesson 4-2: Congruent Triangles Example………… When referring to congruent triangles (or polygons), we must name corresponding vertices in the same order. S U N R A Y R Y SUN  RAY A N U Also NUS  YAR Also USN  ARY S Lesson 4-2: Congruent Triangles

Lesson 4-2: Congruent Triangles Example ……… If these polygons are congruent, how do you name them ? P O U N M E A T S R Pentagon MONTA  Pentagon PERSU Pentagon ATNOM  Pentagon USREP Etc. Lesson 4-2: Congruent Triangles

Lesson 4-2: Congruent Triangles Example ……… Given ΔABC ≅ ΔXYZ , AB = 26, YZ = 30, XY = 4x + 2. Find the value of x. B Y Draw. Label. Get equation. Solve. 4x+2 30 26 A C X Z 4x+2 = 26 4x = 24 x = 6 Lesson 4-2: Congruent Triangles

Lesson 4-2: Congruent Triangles Example ……… Given ΔEFG ≅ ΔPQR , m∠E = 95 , m∠R = 32 , and m∠F = 4x +13. Find the value of x. F Q Draw. Label. Get equation. Solve. 4x+13+95+32=180 4x+140=180 4x=40 x=10 4x+13 32 95 E G P R Lesson 4-2: Congruent Triangles