Triangle Congruence by ASA and AAS Geometry 4-3

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”? B Included Sides

Which side in the following triangle is the “included side”? B Included Sides

Investigating ASA 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 B Investigating ASA

Investigating ASA Copy the marked angle and the two adjacent sides Cut them out, the sides can be any length Investigating ASA

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

Identify The Congruency Describe the following triangle congruence AAS B A Identify The Congruency

Identify The Congruency Describe the following triangle congruence ASA A B Identify The Congruency

Identify The Congruency Describe the following triangle congruence AAS A B Identify The Congruency

Identify The Congruency Describe the following triangle congruence SAS A Identify The Congruency

Identify The Congruency Describe the following triangle congruence SAS A Identify The Congruency

Identify The Congruency Describe the following triangle congruence ASA A B Identify The Congruency

Identify The Congruency Describe the following triangle congruence ASA B A Identify The Congruency

Identify The Congruency Describe the following triangle congruence AAS A B Identify The Congruency

Identify The Congruency Describe the following triangle congruence AAS B A Identify The Congruency

Identify The Congruency Describe the following triangle congruence A AAS B Identify The Congruency

Identify The Congruency Describe the following triangle congruence SAS A Identify The Congruency

Identify The Congruency Describe the following triangle congruence AAA B A C Identify The Congruency

Identify The Congruency Describe the following triangle congruence AAS B A Identify The Congruency

Investigating AAS 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 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

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

Side Side Side congruence 2. Side Angle Side congruence

Angle T Angle C Angle S Angle G

5. SSS Congruence 6. Not enough information given

∠𝐶≅∠𝐹

Yes, SAS Congruence

Yes, ASA Congruence

Yes, SAS Congruence

Yes, SSS Congruence

Yes, SAS Congruence

Yes, SAS Congruence

Yes, AAS

Yes, AAS

Pages 197 – 200 9 – 18, 29, 32 Homework