1. 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 Vocabulary Truths About Triangles MidsegmentsInequalities Relationships In Triangles

2. A segment whose endpoints are at the vertex of a triangle and the midpoint of the side opposite is a… Vocabulary 100

3. Median

4. A perpendicular segment from a vertex to the line containing the side opposite the vertex is called a(n)… Vocabulary 200

5. Altitude

6. A point where three lines intersects is called a(n)… Vocabulary 300

7. Point of Concurrence

8. Vocabulary 400 The point of concurrency of the angle bisectors of a triangle is called the…

9. Vocabulary 400 Incenter

10. Vocabulary 500 The point of concurrency of the altitudes of a triangle is called the…

11. Vocabulary 500 Orthocenter

12. The largest angle of a triangle is across from the _________ side. Truths About Triangles 100

13. Longest Truths About Triangles 100

14. Truths About Triangles 200 Given points and does point C lie on the perpendicular bisector of segment AB?

15. Truths About Triangles 200 Since AC = BC, point C is on the perpendicular bisector because of the perpendicular bisector theorem – point C is equidistant from the endpoints of the segment AB.

16. Truths About Triangles 300 The vertices of a triangle lie at, and Find the center of a circle that would be circumscribed about this triangle.

17. Truths About Triangles 300

18. Truths About Triangles 400 Given and find the coordinates of the midsegment that is parallel to BC.

19. Truths About Triangles 400

20. , and are vertices of triangle PQR.  What are the coordinates of T if is a median of the triangle?  What is the slope of if is the altitude from P?  Tell why or why not is a perpendicular bisector. Truths About Triangles 500

21.  T is the midpoint of , so find the slope of, and take the opposite reciprocal:  Midpoint of Truths About Triangles 500 is the perpendicular bisector

22. Midsegments 100 Find the value of x.

23. Midsegments 100

24. Midsegments 200 Find the value of x.

25. Midsegments 200 60° Equilateral Triangle 5 5

26. Midsegments 300 Find the lengths of AC,CB, and AB.

27. 6 7 5 Midsegments 300

28. Midsegments 400 Find the values of x and y.

29. Midsegments 400

30. Midsegments 500 Marita is designing a kite. The kites diagonals are to measure 64 cm and 90 cm. She will use ribbon to connect the midpoints of its sides that form a pretty rectangle inside the kite. How much ribbon will Marita need to make the rectangle connecting the midpoints?

31. Midsegments 500 The red segments are midsegments of the diagonal that measures 64 cm, so they measure 32 cm. The green segments are midsegments of the diagonal that measure 90 cm, so they measure 45 cm. So the perimeter is

32. Inequalities 100 Name the smallest angle in this triangle

33. Angle B Inequalities 100

34. Inequalities 200 Two sides of a triangle have measure of 12 meters and 22 meters what are the possible measures of the 3 rd side?

35. Inequalities 200

36. Can a triangle have lengths of 2 yards, 9 yards, and 15 yards? Inequalities 300

37. No!

38. If KM = 10, LK = 9 and ML = 18, find the order of the angles from smallest to largest. Inequalities 400

39. Angle M, Angle L, Angle K

40. If KL = x – 4, LM = x + 4 and KM = 2x – 1, and the perimeter of the triangle is 27, find the order of the angles from smallest to largest. Inequalities 500

42. If a point lies on the perpendicular bisector of a segment, what holds true about its distance from the endpoints of the segment? Relationships in Triangles 100

43. The point is equidistant from the endpoints of the segment. Relationships in Triangles 100

44. Solve for x. Relationships in Triangles 200

46. Point C is the centroid of triangle DEF. If GF, G being the midpoint of segment DE, is 9 meters long, what is the length of CF? Relationships in Triangles 300

48. Find the slope of the altitude drawn from vertex A. Relationships in Triangles 400

49. Find the slope of BC. The slope of the altitude drawn from vertex A will have a slope that is the opposite reciprocal of the slope of BC. So the slope of the altitude drawn from vertex A is 2.

50. Find the equation of the line that is the perpendicular bisector of segment CA. Relationships in Triangles 500

51. Step 1: Find the midpoint of CA. Step 2: Find the slope of CA. Step 3: The slope of the perpendicular bisector of CA is the opposite reciprocal of the slope of CA. So the slope of the perpendicular bisector equals. Step 4: Write the equation using point-slope form. Therefore the answer is: