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Transcript
Section 4.2 Apply Congruence and Triangles Goal Identify congruent figures. Congruent figures All the parts of one figure are congruent to the corresponding parts of the other figure. (This means that the corresponding sides and corresponding angles are all congruent) A O CAT DOG C T Corresponding Angles: C D Corresponding Sides: CA DO D G A O T G AT OG CT DG *When writing congruence statements, make sure you ALWAYS list the corresponding vertices in the same order* Example 1: Write a congruence statement for the triangles. Identify all pairs of congruent corresponding parts. a. Angles Sides Example 2: In the diagram, ABCDE FGHIJ. Find the value of x & y. Checkpoint: In Exercises 1 and 2, use the diagram shown in which FGHJ STUV. 1. Identify all pairs of congruent corresponding parts. (2x – 7)° 2. Find the value of x and find mG. Section 4.2 Apply Congruence and Triangles Third Angles Theorem If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also CONGRUENT. Example 3: a. Find mF b. Find mD THEOREM 4.4: PROPERTIES OF CONGRUENT TRIANGLES Reflexive Property of Congruent Triangles Symmetric Property of Congruent Triangles For any triangle ABC, ABC _______ If ABC DEF, then ________________. Sides of Triangles AB _______ Sides of Triangles AB DE, then DE _____ Angles of Triangles A _______ Angles of Triangles A D, then D ____ Transitive Property of Congruent Triangles If ABC DEF, and DEF JKL, then _________________. Angles of Triangles A D and D J, then ___________________________ Example 4: Write a proof. Given: FH JH , FG JG , FHG JHG, FGH JGH Prove: FGH JGH Statements Reasons Section 4.2 Apply Congruence and Triangles