1. Exploring Congruent triangles
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 angles are:
<A≌ <P
<B ≌ <Q
<C ≌ <R
Corresponding sides:
AB ≌ PQ
BC≌ QR
CA≌ RP
∆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
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 Δ PQR ≌ Δ ABC.
3. If Δ ABC ≌ Δ PQR and Δ PQR ≌ Δ TUV,
then Δ ABC ≌ Δ TUV.