Warmup

1. Warmup Solve for x in the picture below: 5x-4 58 3x+22

2. Section 4.1: Congruent Figures LEQ: What are congruent figures and their properties?

3. Pop Quiz write on your note sheet Write never, sometimes or always. • An acute triangle is ____ congruent to an obtuse triangle. • A polygon is ____ congruent to itself. • A right triangle is _____ congruent to another right triangle. • If ∆ABC ≅ ∆XYZ, ∠A is ____ congruent to ∠Y. • If ∆ABC ≅ ∆XYZ, ∠B is ____ congruent to ∠Y.

4. Slides, flips, and turns Congruent figures have the same size and shape. When two figures are congruent, they can be moved so that they fit exactly on top of each other. Examples of movements: Slides Flips Turns

5. What are congruent polygons? What are their properties Talk it over with a partner (no need to write, just brainstorm)

6. Congruent Polygons • Congruent polygons have congruent corresponding parts aka matching sides and angles. • Sides and angles must match up after flipped, turned, or slid. • Order is critical!!

7. Name the corresponding sides and angles <A corresponds to <B corresponds to <C corresponds to A E B F C D <E AC corresponds to ED <F BC corresponds to FD <D AB corresponds to EF

8. If ABCDE  FGHIJ… Corresponding angles/sides are congruent. Order matters in congruency statement. Ex. <A  <F <D  <I CD  HI AE  FJ J F B A C G E D I H

9. Congruent Triangles 3 pairs of congruent angles 3 pairs of congruent sides Congruency statement: ABC  EGR A R G B C E

11. *Applications to Proofs • When the definition of congruent triangles is used in a proof we write, • Corr. parts of Δ’s are or CPCTC !!!

12. Examples of CPCTC If ΔEFG ΔRTW, and this is used in a proof before the last step (meaning we need to use this fact to make other conclusions), then any conclusions we make based off of this congruency statement has the reason “corresponding parts of congruent triangles are congruent or CPCTC”

13. Closure to 4.1 • Go back to pop quiz • An acute triangle is ____ congruent to an obtuse triangle. • A polygon is ____ congruent to itself. • A right triangle is _____ congruent to another right triangle. • If ∆ABC ≅ ∆XYZ, ∠A is ____ congruent to ∠Y. • If ∆ABC ≅ ∆XYZ, ∠B is ____ congruent to ∠Y.

14. Hwk: p. 200-202 1-12, 30-35, 38-40