Exploring Congruent triangles 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 angles are: <A≌ <P <B ≌ <Q <C ≌ <R Corresponding sides: AB ≌ PQ BC≌ QR CA≌ RP ∆ABC≌ ∆PQR The order of letters shows correspondence

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

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.

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

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

Statements: Reasons: 1. AB││CD 2. <EAB ≌<EDC 3 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

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