Obj. 17 Congruent Triangles
- 1. Obj. 17 Congruent Triangles The student is able to (I can): • Identify congruent parts based on a congruence relationship statement • Identify and prove congruent triangles given — Three pairs of congruent sides (Side-Side-Side) — Two pairs of congruent sides and a pair of congruent included angles (Side-Angle-Side)
- 2. Geometric figures are congruent if they are the same size and shape Corresponding shape. angles and corresponding sides are in the same position in polygons with the same number of sides. congruent polygons Two or more polygons whose corresponding angles and sides are congruent. In a congruence statement, the order of the vertices indicates the corresponding parts. Example: Name the corresponding angles if polygon SWIM ≅ polygon ZERO. ∠S ≅ ∠Z; ∠W ≅ ∠E; ∠I ≅ ∠R; ∠M ≅ ∠O
- 3. Example R E C P D A Corresponding Angles Corresponding Sides ∠R ≅ ∠C ED ≅ PA ∠E ≅ ∠P RE ≅ CP ∠D ≅ ∠A RD ≅ CA Thus, ΔRED ≅ ΔCPA.
- 4. Side-Side-Side If three sides of one triangle are congruent Congruence to three sides of another triangle, then the Postulate triangles are congruent. 7 4 T 6 C I 6 4 N P 7 U ΔTIN ≅ ΔCUP
- 5. Example Given: FR ≅ ER , D is the midpoint of FE R Prove: FRD ≅ ERD F Statements 1. 2. 3. 4. FR ≅ ER D is midpt of FE FD ≅ ED RD ≅ RD 5. FRD ≅ ERD D Reasons 1. Given 2. Given 3. Def. of midpoint 4. Refl. prop. ≅ 5. SSS E
- 6. Side-AngleSide Congruence Theorem If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. H U T S L A ΔLHS ≅ ΔUTA
- 7. Example Given: FA ≅ EA , A is the midpoint of RM Prove: FAR ≅ EAM F M A R E Statements 1. FA ≅ EA Reasons 1. Given 2. ∠FAR ≅ ∠EAM 2. Vertical ∠s 3. A is midpt of RM 3. Given 4. RA ≅ MA 4. Def. of midpoint 5. SAS 5. FAR ≅ EAM