1. WARM UP Find the missing angles in the following triangles: 1. 2. 3. Answer the following questions:

2. HOMEWORK ANSWERS 1.Yes 2.No 3.Yes 4.Yes 5.Yes 6.Yes 7.Yes 8.Yes 9.Yes 10. Yes 11. Yes 12. Yes 13. 4 < x < 14 14. 3 < x < 13 15. 4 < x < 16 16. 3 < x < 15 17. 3 < x < 19 18. 3 < x < 25

3. 3.7 MIDSEGMENTS OF TRIANGLES

4. NOTES Midsegment of a Triangle : a segment whose endpoints are the midpoints of two sides.

5. 4 ACTIVITY 1: TRIANGLE MIDSEGMENTS 1.Draw Δ ABC. 2.Find the midpoints, M and N, of sides AB and AC. Then draw MN, the midsegment. 3.Measure and record MN and BC on your paper. What is the relationship between their lengths? 4.Measure and. Measure and. What do your measurements suggest about BC and MN? What postulate or theorem allows you to draw this conclusion? 5.Rewrite and complete the following conjecture: Triangle Midsegment Conjecture A midsegment of a triangle is _______________ to a side of the triangle and has a measure equal to ___________________ of that side. A B C 2 13

6. TRIANGLE CONGRUENCES

7. WHAT DOES IT MEAN FOR TWO FIGURES TO BE CONGRUENT? They must have the same: SIZE SHAPE

8. HERE’S THE SITUATION… Prior to the start of a sailboat race, you (the judging official) must certify that all of the sails are the same size. Without unrigging the triangular sails from their masts, how can the official (you) determine if the sails on each of the boats are the same size? With your group discuss and write down how you would go about doing this? Over the next couple of classes we will be learning some geometry tricks (concepts) involving triangles that will help us answer the above question. Hand out materials

9. ACTIVITY 2: SSS POSTULATE Using these three objects, create a triangle. (The three sides being the ruler, unsharpened pencil and straightedge of the protractor.) Compare your triangle with your group members triangles. What do you notice? Did everyone create the same triangle? Are all of your triangles congruent? Yes Why? All of the parts are the same or congruent. Notice that we did not even pay any attention to the angles and they “took care of themselves” Create another triangle using the three objects, but this time only using 8 inches of the ruler for one of the sides. Are all of your triangles congruent again? Yes With your group discuss how we can use this concept to relate back to our initial problem with the sailboats.

10. SSS (SIDE-SIDE-SIDE) POSTULATE If the sides of one triangle are congruent to the sides of another triangle, then the two triangles are congruent.

11. ACTIVITY 3: SAS POSTULATE 1.Draw a 6 cm segment. 2.Label it GH. 3.Using your protractor, make  G = 60 . 4.From vertex G, draw GI measuring 7 cm long. 5.Label the end point I. 6.From the given information, how many different triangles can be formed? 7.Form  GHI. 8.Is your  GHI congruent to your group members  GHI. 9.What information was used to create this triangle? 10.Draw another segment this time 10 cm long. 11.Label it XY. 12.Using your protractor, make  X = 45 . 13.From vertex X, draw XZ measuring 5 cm long. 14.Label the end point Z. 15.How many different triangles can be formed? 16.Form  XYZ. 17.Is your  XYZ congruent to your group members  XYZ? 18.What information was used to create this triangle?

12. SAS (SIDE-ANGLE-SIDE) POSTULATE If two sides and the included angle in one triangle are congruent to two sides and the included angle in another triangle, then the two triangles are congruent.