1. Activity Each table needs to cut out a perfectly straight sided scalene triangle of any size (larger is better) – (use a straight edge and draw the lines before you cut) Label the largest angle C and the other two A and B Without a ruler, find the midpoint of BC and AC Label those mdpts. L and N and draw LN Fold the triangle on LN Label the point where C meets AB as D Fold both A and B to D Label the vertices M and P 1) What is the relationship between MP and AB? Why? 2) What is the relationship between LN and AB? Why?

2. Relationships within Triangles 5.1 Learning Target: I can identify the special relationships of a midsegment of a triangle and the 3 rd side Success Criteria: I can use relationships of triangles to find lengths of given sides

3. Vocabulary The Midsegment of a Triangle is a segment that connects the midpoints of two sides of the triangle. D B C E A D and E are midpoints DE is the midsegment

4. Theorem 5.1 The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side. Midsegment Theorem D B C E A

5. Example 1 In the diagram, ST and TU are midsegments of triangle PQR. Find PR and TU. PR = ________ TU = ________16 ft 5 ft

6. Example 2 In the diagram, XZ and ZY are midsegments of triangle LMN. Find MN and ZY. MN = ________ ZY = ________53 cm 14 cm

7. Example 3 In the diagram, ED and DF are midsegments of triangle ABC. Find DF and AB. DF = ________AB = ________2652 3X - 4 5X+2 x = ________10

9. Homework Homework p. 288 7,15-23 odds, 25-27 all Challenge - 46