Download G_PP_4-3_CongruenceASAandAAS

Triangle Congruence by
ASA and AAS
Geometry 4-3
• Break one piece of spaghetti into three
similar length sizes.
• Arrange the pieces into a triangle
• How many different triangles can you make?
• Trace each that is different and compare.
Investigation
• An “Included Side” is the
side that is directly between
two angles
Included Sides
• Which side in the following triangle is the
“included side”?
B
A
Included Sides
• Which side in the following triangle is the
“included side”?
B
A
Included Sides
• Which side in the following triangle is the
“included side”?
A
Included Sides
B
• Which side in the following triangle is the
“included side”?
A
B
Included Sides
• Get your supplies
ready
– Ruler
– Marker or pencil
– Two sheets of
Patty Paper
Investigating ASA
• Draw a triangle on one sheet of Patty
Paper
Investigating ASA
• Pick and mark two angles of the triangle
A
B
Investigating ASA
• Copy the marked angle and the two
adjacent sides
• Cut them out, the sides can be any length
Investigating ASA
• Using the Angle – Side - Angle that you
cut out
• Can you form any triangle that is NOT
congruent to the original triangle?
Investigating ASA
• Is it possible to form a new triangle that
is NOT congruent to your original
triangle?
• This is called Angle-Side-Angle
congruence
Investigating ASA
ASA Congruence
AAS
Triangle Congruence
• An “Non-Included Side” is the side that is
Adjacent to two angles
Non-Included Sides
• Describe the following triangle
congruence
AAS
B
A
Identify The Congruency
• Describe the following triangle
congruence
ASA
B
A
Identify The Congruency
• Describe the following triangle
congruence
AAS
A
B
Identify The Congruency
• Describe the following triangle
congruence
SAS
A
Identify The Congruency
• Describe the following triangle
congruence
SAS
A
Identify The Congruency
• Describe the following triangle
congruence
ASA
A
B
Identify The Congruency
• Describe the following triangle
congruence
ASA
B
A
Identify The Congruency
• Describe the following triangle
congruence
AAS
A
B
Identify The Congruency
• Describe the following triangle
congruence
AAS
B
A
Identify The Congruency
• Describe the following triangle
congruence
AAS
A
B
Identify The Congruency
• Describe the following triangle
congruence
SAS
A
Identify The Congruency
• Describe the following triangle
congruence
AAA
B
C
A
Identify The Congruency
• Describe the following triangle
congruence
AAS
B
A
Identify The Congruency
• Get your supplies
ready
– Ruler
– Marker or pencil
– Two sheets of
Patty Paper
– Scissors
Investigating AAS
• Draw a triangle on one sheet of Patty
Paper
Investigating AAS
• Pick and mark two angles of the triangle
A
B
Investigating AAS
• Mark an adjacent side
A
B
Investigating AAS
• Copy the marked side, and its adjacent
angle only onto a piece of patty paper
• Cut it out
Investigating AAS
• Copy the OTHER angle onto a piece of
patty paper, cut it out
Investigating AAS
• Using the Angle – Angle - Side that you
cut out
• Can you form any triangle that is NOT
congruent to the original triangle?
Investigating AAS
AAS Congruence
1. Side Side Side congruence
2. Side Angle Side congruence
1. Angle T
2. Angle C
3. Angle S
4. Angle G
5. SSS Congruence
6. Not enough information given
C  F
AC  DE
AC  DE
CB  EF
A  D
Yes, SAS Congruence
Yes, ASA Congruence
Yes, SAS Congruence
Yes, SSS Congruence
Yes, SAS Congruence
Yes, SAS Congruence
Yes, AAS
Yes, ASA
Yes, AAS
Yes, SAS
Yes, ASA
Yes, AAS
• Pages 197 – 200
• 9 – 18, 29, 32
Homework
• Pages 197 – 200
• 9 – 18, 28, 29, 32
Honors Homework