 In this unit, you will learn:  How to support a mathematical statement using flowcharts and conditional statements.  About the special relationships.

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Presentation transcript:

 In this unit, you will learn:  How to support a mathematical statement using flowcharts and conditional statements.  About the special relationships between shapes that are similar or congruent.  How to determine if triangles are similar or congruent.  3.1 Prove Triangle Similarity  I can prove two triangles are similar. G.3.B, G.1.F  This means I can  Use a flow chart, two-column proof, or paragraph proof to demonstrate the steps needed to prove that two triangles are similar  Determine if two triangles are similar using triangle similarity conjectures (AA~, SAS~, SSS~)  CPM Materials:   Will need extra practice  State EOC Examples:  For a given ∆RST, prove that ∆XYZ, formed by joining the midpoints of the sides of ∆RST, is similar to ∆RST.  . 

 Similar figures have the SAME SHAPE.  Corresponding sides are PROPORTIONAL.

 Same SHAPE…right? How can you tell if they are the same shape?  Corresponding angles are equal.  Corresponding sides are proportional.

AA stands for "angle, angle" and means that the triangles have two of their angles equal.  If two triangles have two of their angles equal, the triangles are similar. 

 If two of their angles are equal, then the third angle must also be equal, because angles of a triangle always add to make 180°.angles of a triangle always add to make 180°  In this case the missing angle is: 180° - (72° + 35°) = 73°. So AA could also be called AAA.

 SSS stands for "side, side, side" and means that we have two triangles with all three pairs of corresponding sides in the same ratio (proportional).  For example:

Chapter 3 Problems 45-46, 48-52

Proof Video Clip

Ch. 3 (53-55, 57,59-63) Check your answers in your group. Any troubles, write the # on the board.

1) Angle-Angle similarity (AA~) 2) Side-Side-Side similarity (SSS~)

If they are the same shape and same size, we say they are CONGRUENT.

Ch. 3 (64, in class & 68-72)

Write the “problem” problems on the board.

SAS stands for "side, angle, side" and means that we have two triangles where: ◦ the ratio between two sides is the same as the ratio between another two sides ◦ and we we also know the included angles are equal.

If two triangles have two pairs of sides in the same ratio and the included angles are also equal, then the triangles are similar.

Why doesn’t ASS or SSA work?ASS or SSA

Ch. 3 (74-76, 78-82)

Ch. 5(94-100)