This document discusses different postulates for proving that two triangles are congruent, including: side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), and angle-angle-side (AAS). It provides examples of applying each postulate to determine if two triangles are congruent and identifies that there are no angle-angle-angle (AAA) or side-side-angle (SSA) postulates. The document also has exercises for the reader to practice using the postulates to determine if pairs of triangles are congruent.
4. . . . about two triangles
to prove that they
are congruent?
Corresponding Parts
In Lesson 4.2, you learned that if all
six pairs of corresponding parts (sides
5. and angles) are congruent, then the
triangles are congruent.
• AB ≅ DE
• BC ≅ EF
• AC ≅ DF
D∆ABC ≅ ∆
∀ ∠ A ≅ ∠
DEF
∀ ∠ B ≅ ∠ E
32. Let’s Practice
Indicate the additional information needed
to enable us to apply the specified
congruence postulate.
For ASA:
∠B ≅ ∠D
For SAS:
AC ≅ FE
33. For AAS: ∠A ≅ ∠F
Indicate the additional information needed
to enable us to apply the specified
congruence postulate.
35. Determine if whether each pair of triangles is congruent by
SSS, SAS, ASA, or AAS. If it is not possible to prove
that they are congruent, write not possible.
Ex 4 GK
H J
I
36. ΔGIH ≅ ΔJIK by AAS
Determine if whether each pair of triangles is congruent by
SSS, SAS, ASA, or AAS. If it is not possible to prove
that they are congruent, write not possible.
38. ΔABC ≅ ΔEDC by
ASA
Determine if whether each pair of triangles is congruent by
SSS, SAS, ASA, or AAS. If it is not possible to prove
that they are congruent, write not possible.
Ex 6 AE
41. Determine if whether each pair of triangles is congruent by
SSS, SAS, ASA, or AAS. If it is not possible to prove
that they are congruent, write not possible.
Ex 7 K
M L
J
42. ΔJMK ≅ ΔLKM by SAS or
ASA
Determine if whether each pair of triangles is
congruent by SSS, SAS, ASA, or AAS. If it is
not possible to prove that they are congruent,
write not possible.
Ex 8
JT