1. Define a Trapezoid. What Formula Would You Use to Prove a Trapezoid?

Study Guide for chapter 9Put answers on SEPARATE SHEET OF PAPER.

1. Define a trapezoid. What formula would you use to prove a trapezoid?

2. Name 3 different types of triangles based on side lengths. What type of formula is used to classify?

3. Name 3 different types of triangles based on angle measure. Which theorem and formula is used to classify?

4. Given a point and an equation of a circle, how does one figure out whether a point is inside, on or outside a circle? What formula is used?

5. Know how to GRAPH a circle given a standard equation.Pg 404 #33-35

6. Know how to write a standard equation of a circle given a graph.Pg 404 #24-25

7. Given a standard equation, identify the radius and the center.Pg 404 #20-23

8. How do we define a quadrilateral by its sides? Specify your formula.

9. How do you know if a quadrilateral is a parallelogram? Specify your formula.

10. Name two ways you can figure out if a parallelogram is a rectangle and specify the formulae you would use.

11. Given the coordinates of the vertices of a triangle, how can one easily find a centroid?

12. How does one demonstrate that a line inside a triangle is a median? Specify your formula.

13. How does one demonstrate that a line inside a triangle is an altitude? Specify your formula.

14. If two lines bisect each other, then the two lines must have different ______and the intersection point should be the ______of each line.

15. How does one find the area of a parallelogram?

16. If point X is the same distance from point A and point C, then we call that point the _.

17. Translate the formula x2 + y2 = 9 by 6 units left and 5 units up.

18. How does one show that a quadrilateral is a rhombus by showing it is a parallelogram with perpendicular diagonals? Specify the formula used.

19. Given the diameter endpoints of (2,5) and (10, -1) find the center of the circle, the radius, and give the standard formula.

20.Write a coordinate proof showing that the diagonals of a rectangle not a square are not perpendicular.

21. Write a coordinate proof of the following theorem: If a parallelogram is a rectangle, then its diagonals are congruent.

22.Prove using coordinate geometry: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

23. Given Triangle ABC with coordinates A(1,3) B (3,0) and C (-2,-2):

a. Find the equation of the altitude that goes through vertex C.

b. Find the intersection point of this altitude and line segment AB.

c. Find the length of the altitude and the area of the triangle.

24. What is the concurrency of medians theorem? Which formula would aid you in your use of this theorem?