1. Geometry - 4.3 Congruent Triangles

2. Congruent, Corresponding Angles/Sides Two figures are congruent when their corresponding sides and corresponding angles are congruent. Corresponding Angles Corresponding Sides There is more than one way to write a congruence statement, but the you must list the corresponding angles in the same order.

4. Naming Congruent Parts Write a congruence statement for the triangles below. Identify all pairs of congruent parts. Corresponding Angles Corresponding Sides

5. Identify Corresponding Congruent Parts Show that the polygons are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement. Answer: All corresponding parts of the two polygons are congruent. Therefore, ABCDE  RTPSQ . Sides: Angles:

6. Third Angle Thm Third Angle Thm. - If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. If and then,

7. Properties of Congruent Triangles Transitive Property of Congruent Triangles Reflexive Property of Congruent Triangles Symmetric Property of Congruent Triangles

10. Using the Third Angle Thm. Find the value of x.

11. Determining Triangle Congruency Decide whether the triangles are congruent. Justify your reasoning. From the diagram all corresponding sides are congruent and that <F and <H are congruent. <EGF and <HGJ are congruent because of Vertical angles. <E and <J are congruent because of the third angle theorem Since all of the corresponding sides and angles are congruent,

13. Use Corresponding Parts of Congruent Triangles In the diagram, Δ ITP  Δ NGO . Find the values of x and y .  O   P 6 y – 14 = 40 6 y = 54 y = 9 x – 2 y = 7.5 x – 2(9) = 7.5 x – 18 = 7.5 x = 25.5 Answer: x = 25.5, y = 9

14. A. x = 4.5, y = 2.75 B. x = 2.75, y = 4.5 C. x = 1.8, y = 19 D. x = 4.5, y = 5.5 In the diagram, Δ FHJ  Δ HFG . Find the values of x and y .

15. Proof: Prove: Δ LMN  Δ PON 2.  LNM   PNO 2. Vertical Angles Theorem Statements Reasons 3.  M   O 3. Third Angles Theorem 4. Δ LMN  Δ PON 4. Def of Congruent Triangles 1. Given 1.