Geometry 4-3 Triangle Congruence by ASA and AAS. Investigation Break one piece of spaghetti into three similar length sizes. Arrange the pieces into a.

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Presentation transcript:

Geometry 4-3 Triangle Congruence by ASA and AAS

Investigation 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.

Included Sides An “Included Side” is the side that is directly between two angles

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

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

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

Which side in the following triangle is the “included side”? A 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 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

ASA Congruence

Triangle Congruence AAS

Non-Included Sides An “Non-Included Side” is the side that is Adjacent to two angles

Describe the following triangle congruence A B Identify The Congruency AAS

Describe the following triangle congruence A B Identify The Congruency ASA

Describe the following triangle congruence A B Identify The Congruency AAS

Describe the following triangle congruence A Identify The Congruency SAS

Describe the following triangle congruence A Identify The Congruency SAS

Describe the following triangle congruence A B Identify The Congruency ASA

Describe the following triangle congruence A B Identify The Congruency ASA

Describe the following triangle congruence A B Identify The Congruency AAS

Describe the following triangle congruence A B Identify The Congruency AAS

Describe the following triangle congruence A B Identify The Congruency AAS

Describe the following triangle congruence A Identify The Congruency SAS

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

Describe the following triangle congruence A B Identify The Congruency AAS

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 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?

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

Yes, SAS Congruence

Yes, ASA Congruence

Yes, SAS Congruence

Yes, SSS Congruence

Yes, SAS Congruence

Yes, AAS

Yes, ASA

Yes, AAS

Yes, SAS

Yes, ASA

Yes, AAS

Homework Pages 197 – – 18, 29, 32

Honors Homework Pages 197 – – 18, 28, 29, 32