The Five Ways to Prove
that 2 Triangles are
Congruent
Objectives
Prove that triangles are congruent
using the SSS, SAS, ASA, AAS , and HL
Congruence Postulates
Side-Side-Side (SSS)
Congruence Postulate B
If three sides of E
one triangle are C
congruent to three A
sides of a second F
D
triangle, then the
two triangles are If Side AB FE,
congruent. Side BC ED
Side AC FD
Then ABC FED
Side-Angle-Side (SAS)
Congruence Postulate
If 2 sides and the B E
included angle of
one triangle are C
F
D
congruent to 2
A
sides and the If Side AB FE,
included angle of Angle A F
the second triangle,
then the 2 triangles Side AC FD
are congruent
Then ABC FED
Angle-Side-Angle (ASA)
Congruence Postulate
B
If 2 angles and the
included side of one E
triangle are C
congruent to 2 A
angles and the D
included side of a F
second triangle, If Angle A F
then the two
triangles are Side AC FD
congruent Angle C D
Then ABC FED
Angle-Angle-Side (AAS)
Congruence Postulate
B
If 2 angles and a
nonincluded side of E
one triangle are C
congruent to two A
angles and the D
corresponding F
nonincluded side of a If Angle A F
second triangle, then
the two triangles are Angle C D
congruent Side BC ED
Then ABC FED
Hypotenuse-Leg (HL)
Congruence Postulate
A
If the hypotenuse
and a leg of a right
triangle are
C
congruent to the B
D
hypotenuse and a
leg of a second
triangle, then the 2
E
triangles are F
congruent If BC EF and AC DF
Then, ABC DEF
State which congruence method (SSS, SAS, ASA, AAS, HL) can be
used to prove the triangles congruent. If no method applies, write
“none”.
B C
Given: BC || AD ; BC DA
(a) Mark all congruencies in
the figure.
A D
(b) Why are the triangles congruent? SSS SAS ASA AAS HL
(c) List the three congruencies used for your answer to part (b)
(d) Complete the congruency statement: ABC ________
Given: AB || DE ; A D ; AC DB A D
(a) Mark all congruencies in
the figure. C B E
(b) Why are the triangles congruent? SSS SAS ASA AAS HL
(c) List the three congruencies used for your answer to part (b)
(d) Complete the congruency statement: ABC ________
Given: AE BD ; C is the midpoint of DB ; A B
AB ED
C
(a) Mark all congruencies in
the figure.
D E
(b) Why are the triangles congruent? SSS SAS ASA AAS HL
(c) List the three congruencies used for your answer to part (b)
(d) Complete the congruency statement: ABC ________
Assignment
pg. 223: 2-4, 8-13
pg. 224: 19
Write a complete proof including figure,
Given, Prove, Statements and
Reasons. Be sure to label your
Statements and Reasons.
Quiz on 4.1, 4.2