1. 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

2. Remember Proofs? Five ways to say two triangles are congruent: 1. SSS
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.

3. 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 Prove: AB DE D A C B E

4. Example #2: Given: Parallelogram ABCD Prove: AEB DEC A B E D C
Aim 6.5: To prove two triangles in a Quadrilateral are congruent
Example #2:
Given: Parallelogram ABCD Prove: AEB DEC A B E D C

5. Example: #3 Given: Parallelogram PQRS PE SQ & RF SQ Prove: SE QF P Q F
Aim 6.5: To prove two triangles in a Quadrilateral are congruent
Example: #3
Given: Parallelogram PQRS PE SQ & RF SQ Prove: SE QF P Q F E S R

6. Aim 6.5: To prove two triangles in a Quadrilateral are congruent
Example #3:
Statement Reason
Parallelogram PQRS 1. Given
PS QR 2. Opposite sides of a p-gram are
PS || QR Opposite sides of a p-gram are ||
Angle PSE Angle RQF 4. Alternate interior angles are
PE SQ & RF SQ 5. Given
Angle PES & Angle RFQ 6. Perpendicular lines
are right angles form right angles
Angle PES Angle RFQ 7. All right angles are
PES RFQ 8. AAS
SE QF 9. CPCTC

7. Example #4: Packet page 1 #1
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 B 1 2 D C F E

8. 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: