Each member of your table will complete this activity independently of his partners/team members, but will join in a discussion following the construction portion of each activity.

Activity #1
Choose three segment lengths for this activity, making sure each team member chooses different lengths between 2cm and 5cm.

1. Draw  DABC so that all three sides are between 2cm and 5cm in length.
2. Construct DXYZ so that it is NOT congruent to DABC ( DABC ¹ DXYZ ), but make 2 corresponding angles congruent. For example ÐA @ ÐX and ÐC @ ÐZ.
3. Measure the lengths of the sides and angles on each triangle and record your measurements in a data table.
   

   item	1st angle ÐA ( ÐX)	2nd angle ÐB ( ÐY)	3rd angle ÐC ( ÐZ)	1st side AB (XY)	2nd Side BC (YZ)	3rd Side AC (XZ)
   DABC
   DXYZ

4. Compute the ratios of the corresponding sides to the nearest tenth and determine the scale factor for your two triangles.
5. Compare your results with those of your team and discuss the "points to ponder" then come up with a "TEAM ANSWER" to each question.

Points to Ponder

• If you know that two of the corresponding angles are congruent, why must the third angles also be equal in measure ?
• Are the two triangles similar ? (Is DABC ~ DXYZ ).
  
• Make a conjecture about two triangle with two corresponding angles that have the same measure.

Problem to complete

Construct a triangle  DMNO with the sides 2cm, 3cm, & 4cm long then explain how you would construct a triangle  DGHK similar to  DMNO with a scale factor of 3. Then do it !

 

Activity #2
Choose three segment lengths for this activity, making sure each team member chooses different lengths between 4cm and 8cm.

1. Draw  DABC so that all three sides are between 4cm and 8cm in length.
2. Use a ruler or a compass to extend  sides AB and AC of the triangle to construct new segments AB' and AC', so that these new segments are now twice their original size (AB' = 2AB).Then Connect B' to C' making a new triangle AB'C'.
3. Measure each segment and angle and record the information in a data table just like you did in activity #1.
4. Compute the ratios of the corresponding sides to the nearest tenth and determine the scale factor for your two triangles.
5. Compare your results with those of your team and discuss the "points to ponder" then come up with a "TEAM ANSWER" to each question.

Points to Ponder

• Are the sides of the two triangles proportional ? If so, what is the scale factor?
• What is the relationship of  the corresponding angles ?
• Are the two triangles similar ? (Is DABC ~ DAB'C' ).
• Make a conjecture about two triangle with two corresponding angles that have the same measure.

Problem to complete

Use DMNO that you constructed in activity #1 to complete this problem.  Demonstrate your conjecture by explaining how you would construct a triangle  DRST similar to DMNO with a scale factor of 4.

Activity #3
Use DABC from activity #1 to complete this activity.

1. Re-Draw  DABC and then   locate the mid point of each side by accurate measurement or by constructing the perpendicular bisectors of each side.
2. Copy ÐB and redraw it. Label this new angle ÐY.
3. Construct YD half the length of AB.
4. On the other side of ÐY, construct YE half the length of BC.
5. Complete DDYE. Use a protractor and ruler to measure the angles/sides. Complete the data table below.
6. Compute the ratios of the corresponding sides to the nearest tenth and determine the scale factor for your two triangles.
7. Compare your results with those of your team and discuss the "points to ponder" then come up with a "TEAM ANSWER" to each question.

Points to Ponder

• Are the sides of the two triangles proportional ? If so, what is the scale factor?
• What is the relationship of  the corresponding angles ?
• Are the two triangles similar ? (Is DABC ~ DAB'C' ).
• Make a conjecture about two triangle with two corresponding angles that have the same measure.

Problem to complete

Use DMNO that you constructed in activity #1 to complete this problem.  Demonstrate your conjecture by explaining how you would construct a triangle  DRST similar to DMNO with a scale factor of 4.