Warm Up Find the measures of the sides of ∆ABC and classify the triangle by its sides. A(-7, 9) B(-7, -1) C(4, -1) AB = 10 BC = 11 AC = √221 The triangle is scalene.

FG, GH, FH, F, G, H Warm Up 1. Name all sides and angles of ∆FGH. 2. What is true about K and L? Why? 3. What does it mean for two segments to be congruent? FG, GH, FH, F, G, H  ;Third s Thm. They have the same length.

Congruent Triangles Section 4-3

Congruent Triangles Same size. Same shape. All 6 corresponding parts (angles and sides) of two triangles are congruent. CPCTC: “Corresponding parts of congruent triangles are congruent. Example: If ∆ABC  ∆DEF, then…

Example: Naming Congruent Corresponding Parts Given: ∆PQR  ∆STW Identify all pairs of corresponding congruent parts. Angles: P  S, Q  T, R  W Sides: PQ  ST, QR  TW, PR  SW

Example: Using Corresponding Parts of Congruent Triangles Given: ∆ABC  ∆DBC. Find the value of x. x = 53

Example: Given: ∆ABC  ∆DEF Find the value of x. Find mF. x = 4

Triangle Congruence Theorem Congruence of triangles is: Reflexive Symmetric Transitive

Congruence Transformations To slide (translate), flip (reflect), or turn (rotate) triangles does not change their size or shape. ∆ABC → ∆A'B'C'

Example: Proving Triangles Congruent Given: YWX and YWZ are right angles. YW bisects XYZ. W is the midpoint of XZ. XY  YZ. Prove: ∆XYW  ∆ZYW

Statements Reasons 1. YWX and YWZ are rt. s. 1. Given 2. YWX  YWZ 2. All Rt.  are  3. YW bisects XYZ 3. Given 4. XYW  ZYW 4. Def. of bisector 5. W is mdpt. of XZ 5. Given 6. XW  ZW 6. Def. of mdpt. 7. Reflex. Prop. of  7. YW  YW 8. X  Z 8. Third s Thm. 9. XY  YZ 9. Given 10. ∆XYW  ∆ZYW 10. Def. of  ∆

Lesson Quiz 1. ∆ABC  ∆JKL and AB = 2x + 12. JK = 4x – 50. Find x and AB. Given that polygon MNOP  polygon QRST, identify the congruent corresponding part. 2. NO  ____ 3. T  ____ 31, 74 RS P