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Section 4.1

Section 4.1. Exploring Congruent triangles. Definition of Congruent Triangles. If Δ ABC is congruent to Δ PQR, then there is both an angle and side correspondence. Corresponding sides: AB ≌ PQ BC≌ QR CA≌ RP. Corresponding angles are: <A ≌ <P <B ≌ <Q <C ≌ <R. ∆ABC≌ ∆PQR.

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Section 4.1

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  1. Section 4.1 Exploring Congruent triangles

  2. Definition of Congruent Triangles If Δ ABC is congruent to Δ PQR, then there is both an angle and side correspondence. Corresponding sides: AB ≌ PQ BC≌ QR CA≌ RP Corresponding angles are: <A≌ <P <B ≌ <Q <C ≌ <R ∆ABC≌ ∆PQR The order of letters shows correspondence

  3. Classification of Triangles • By sides • Equilateral triangle- three congruent sides • Isosceles triangle-at least two congruent sides • Scalene triangle-no sides are congruent • By angles • Acute triangle-has three acute angles • Right triangle-has one 90°(right angle) • Obtuse Triangle-has exactly one obtuse angle • Equiangular Triangle-has all three angles are equal

  4. Triangles In ∆ABC, each of the points A, B, and C is a vertex of the triangle. The side BC is the side opposite <A Two sides that share a common vertex are adjacent sides.

  5. Triangles In a right triangle, we have legs and hypotenuse In an isosceles triangle, have legs and base

  6. Prove the following: • Given: AB≌CD, AB││CD • E is the midpoint of BC and AD Prove: ∆AEB≌∆DEC

  7. Statements: Reasons: 1. AB││CD 2. <EAB ≌<EDC 3.<ABE ≌<DCE 4.<AEB≌<CED 5. AB≌ CD 6. E is the midpoint of AD 7. AE ≌ ED 8. E is the midpoint of BC 9. BE ≌ EC 10. ∆AEB ≌ ∆DEC

  8. Theorem 4.1 • Properties of Congruent Triangles 1. Every triangle is congruent to itself. 2. If Δ ABC ≌Δ PQR, then ΔPQR ≌Δ ABC. 3. If ΔABC ≌Δ PQR and Δ PQR ≌Δ TUV, then Δ ABC ≌ΔTUV.

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