Congruent Triangle Shortcuts DO NOW 11/17: How can you create two congruent triangles from the kite below? Use the properties of a kite to explain your answer. Congruent Triangle Shortcuts Agenda Congruence and Rigid Motion Corresponding Parts and Tips SSS and SAS Exit Ticket/Debrief

Congruence and Polygons Two figures are congruent if they have exactly the same size and shape. Two polygons are congruent if they have congruent corresponding sides and angles Specifically,  triangles have 3  corresponding sides and 3  corresponding <s A C B D E F *MUST BE IN NOTES!*

Rigid Motions and Congruence Since rigid transformations move every point the same way, the resulting figure remains congruent. Translations, rotations and reflections all result in congruent images. Therefore, if we can transform a figure to land on top of itself, we can identify the parts of that figure that are corresponding and congruent. B A C B A C

Corresponding Parts If all 6 pairs of corresponding parts (sides and angles) are , then the triangles are . B A C AB  DE BC  EF AC  DF  A   D  B   E  C   F ABC   DEF E D F

Steps and Tricks a) Reflexive Sides b) Vertical Angles 1. Mark everything that is given 2. BEWARE OF and MARK: a) Reflexive Sides (remember Reflexive Property of Congruence: AB  AB) b) Vertical Angles (across from each other and  ) 3. Look for short-cuts that match the theorems *MUST BE IN NOTES!*

Do you need all 6 ? NO ! SSS SAS ASA AAS

Side-Side-Side (SSS) AB  DE BC  EF AC  DF ABC   DEF SSS: If 3 sides of 1 triangle are  to 3 sides of another triangle, then the 2 triangles are . *MUST BE IN NOTES!*

Side-Angle-Side (SAS) B F A D C AB  DE A   D AC  DF ABC   DEF included angle SAS: If 2 sides of 1 triangle are  to 2 sides of another triangle and the included < of 1 triangle is  to the included < of another triangle, then the 2 triangles are . *MUST BE IN NOTES!*

Included Angle Is the < between or INside 2 sides  H  G  I

Included Angle Name the included angle: YE and ES ES and YS YS and YE

Name That Postulate (when possible) SAS SAS ASS SSS

Name That Postulate SAS SAS ASS SAS Vertical Angles Reflexive Property (when possible) Vertical Angles Reflexive Property SAS SAS Vertical Angles Reflexive Property ASS SAS

Triangle Congruence Shortcuts #2 DO NOW 11/18: Triangle Congruence Shortcuts #2 Agenda HW Review ASA and AAS Algebra Practice Debreif/Exit

Angle-Side-Angle (ASA) B E F A C D A   D AB  DE  B   E ABC   DEF Included side ASA: If 2 <s of 1 triangle are  to 2 <s of another triangle and the included side of 1 triangle is  to the included side of another triangle, then the 2 triangles are .

Included Side The side between two angles GI GH HI

Included Side Name the included side: Y and E E and S S and Y YE ES SY

Example From the information in the diagram, can you prove that ΔFDG and ΔFDE are congruent? Explain. yes; AAA yes; ASA yes; SSS no

Angle-Angle-Side (AAS) B E F A C D A   D  B   E BC  EF ABC   DEF Non-included side AAS: If 2 <s of 1 triangle are  to 2 <s of another triangle and the non-included side of 1 triangle is  to the non-included side of another triangle, then the 2 triangles are .

There is no such thing as an ASS postulate! Warning: No ASS Postulate There is no such thing as an ASS postulate! NOT CONGRUENT

There is no such thing as an AAA postulate! Warning: No AAA Postulate There is no such thing as an AAA postulate! E B C A F D NOT CONGRUENT

The Congruence Postulates SSS correspondence ASA correspondence SAS correspondence AAS correspondence ASS correspondence AAA correspondence

Name That Postulate (when possible) SAS ASA ASS SSS

Name That Postulate (when possible) AAA ASA ASS SAS

Determine which triangles are congruent by AAS using the information in the diagram below. ΔABE ≅ ΔCBE ΔABF ≅ ΔEDF ΔABE ≅ ΔEDA ΔADC ≅ ΔEBC Name the postulate that proves that the triangles are congruent. (Hint: What type of triangle is this and what are its special properties?) SAS AAS ASA ASS

Let’s Practice B  D AC  FE A  F Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: B  D For SAS: AC  FE A  F For AAS:

Transformations and Congruence DO NOW 11/19: Identify if the two triangles are congruent using a congruence shortcut. Then solve for x. (3x+5) cm 26 cm Transformations and Congruence Agenda Note Check/HW CPCTC GeoGebra Investigation Exit Ticket/Debrief

CPCTC (Corresponding Parts of Congruent Triangles are Congruent) Once we use congruence shortcuts to identify that two triangles are congruent, we know that ALL corresponding parts of those triangles are congruent.

Debrief: Transformations and Proving Triangle Congruence How can we use transformations to show that our triangle congruence shortcuts work? How would we use a formal two column proof to show that two triangles are congruent?

Flow Chart Proof DO NOW 11/20: Label the diagram with the given information. What congruence shortcut can we use to prove that AB and DC are parallel? Flow Chart Proof Agenda Congruence Shortcuts Quiz Flow Chart Proof Flow Chart Example Debrief

Flow Chart Proofs Like a two column proof, flow chart proofs start with given information and use logic to arrive at a conclusion (“prove”) Flow charts contain statements (boxes) that must be supported by reasons (lines underneath boxes)

Flow Chart Proof (Do Now)

Flow Chart Proof (Independent Practice)

Debrief What are some advantages/disadvantages to flow chart proof over two-column proofs?