Aim 6.5: To prove two triangles
in a Quadrilateral are congruent
Do Now: (Show all work)
1. Determine the number of degrees on an
interior angle in a polygon with 8 sides:
2. What is the measurement of an exterior
angle of a 9 sided polygon?
Homework: Packet Page 12 #2 & 3
Aim 6.5: To prove two triangles in a Quadrilateral are congruent
Remember Proofs?
• Five ways to say two triangles are congruent:
1. SSS
2. SAS
3. ASA
4. AAS
5. HL
• Angles can be congruent because of perpendicular
and parallel lines
• Bisectors and medians create congruent
sides
• Always look to prove 2 triangles are
congruent first. Then you can use CPCTC.
Aim 6.5: To prove two triangles in a Quadrilateral are congruent
Example #1:
Given: Triangles ABC & CDE
C is the midpoint of BD
AB is parallel to DE
A
Prove: AB
DE
D
C
B
E
Aim 6.5: To prove two triangles in a Quadrilateral are congruent
Example #2:
Given: Parallelogram ABCD
Prove:
AEB
A
DEC
B
E
D
C
Aim 6.5: To prove two triangles in a Quadrilateral are congruent
Example: #3
Given: Parallelogram PQRS
PE
SQ & RF
SQ
Prove: SE
P
QF
Q
F
E
S
R
Aim 6.5: To prove two triangles in a Quadrilateral are congruent
Example #3:
Statement
1. Parallelogram PQRS
2. PS
QR
3. PS || QR
4. Angle PSE
Angle RQF
5. PE
SQ & RF
SQ
6. Angle PES & Angle RFQ
are right angles
7. Angle PES
Angle RFQ
8.
PES
RFQ
9. SE
QF
Reason
1. Given
2. Opposite sides of a
p-gram are
3. Opposite sides of a
p-gram are ||
4. Alternate interior
angles are
5. Given
6. Perpendicular lines
form right angles
7. All right angles are
8. AAS
9. CPCTC
Aim 6.5: To prove two triangles in a Quadrilateral are congruent
Example #4:
Packet page 1 #1
Given: Rectangle ABCD
DF CE
Prove: a) ADE
BCF
b) Angle 1 Angle 2
c) GF
GE
A
D
B
1
F
2
E
C
Aim 6.5: To prove two triangles in a Quadrilateral are congruent
Exit Ticket:
• True or False: The opposite sides of a
Parallelogram are congruent but not parallel
• We can say AC
AC by _____________
• Name the 5 methods we can use to prove two
triangles are congruent: