Warm Up Find the measures of the sides of ∆ ABC and classify the triangle by its sides.

1. 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.

2. 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?  ;Third s Thm. They have the same length.

3. Congruent Triangles Section 4-3

4. 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…

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

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

7. Example: Given: ∆ABC  ∆DEF Find the value of x. x = 4 Find mF. mF = 37°

8. Triangle Congruence Theorem • Congruence of triangles is: • Reflexive • Symmetric • Transitive

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

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

11. 5.W is mdpt. of XZ 6.XW ZW 7.YW YW 9.XY YZ 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. Given 6. Def. of mdpt. 7. Reflex. Prop. of  8.X  Z 8. Third s Thm. 9. Given 10.∆XYW  ∆ZYW 10. Def. of  ∆

12. RS 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 P