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
∆ABC≌ ∆PQR
BC≌ QR
The order of letters
CA≌ RP
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:
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
Reasons:
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.