Name: Date: Period: Chapter 11: Coordinate Geometry Proofs Review Sheet Complete the entire review sheet (on here, or separate paper as indicated) h in on test day for 5 bonus points! Part 1 The Quadrilateral Family Tree Directions: Answer each question as True or False on the line provided. (a) Parallelograms are never trapezoids. (c) All parallelograms are rectangles. (e) Isosceles trapezoids are trapezoids. (g) In a square all sides are congruent. (i) Parallel sides of an isosceles trapezoid are congruent. (j) All quadrilaterals have 4 congruent sides (b) All squares are rhombuses. (d) A rhombus is a rectangle. (f) A square is a rectangle. (h) A rectangle is a square. Part 2 Coordinate Geometry Multiple Choice Questions Directions: Answer each question on the line provided. Show all work in your notebook. 1) A line segment has endpoints What is the length of the segment? (1) (2) (3) (4 2) A line segment has endpoints What are the coordinates of the midpoint? 3) What is the slope of a line that is perpendicular to the equation is? 4) In circle O, a diameter has endpoints What is the length of the diameter? 5) The equation of line k is. The equation of line m is The lines are: (1) parallel (2) perpendicular (3) the same (4) neither 6) Segment AB is the diameter of circle M. The coordinates of A are M are What are the coordinates of B? The coordinates of 7) What is the equation of a line passing through parallel to 8) If is the midpoint of is is find the coordinates of B. 9) Classify the two lines represented by the equation (1) parallel (2) perpendicular (3) the same (4) neither 10) Find the midpoint of the segment joining the points
Part 3 Coordinate Geometry Short Answer Questions Directions: Answer each question in the space provided. Show all work in your notebook. 1) Given the points (-4,12) (-6,8), find the distance (in simplest radical form), midpoint, slope. 2) Given A(6,5) B(10,6), C(2,6) D(4,-2), how are lines AB CD related? 3) Find the slope of a line parallel to. 4) Find the slope of a line perpendicular to. 5) What is the equation of a line that is parallel to passes through the point (-4,8). 6) Given the following pentagon, find: 7) Given triangle ABC with vertices A(-3,2), B(-6,5), (a) Perimeter C(-1,4). (b) Area a) Find the coordinates of D, the midpoint of AB. b) Find the coordinates of E, the midpoint of AC. c) Find the length of DE BC. d) How are AB AC related? 8) Write an equation of the perpendicular bisector of the line segment whose endpoints are (4,8) (-6,10). Part 4 Quadrilateral Proofs. Directions: Using your knowledge of quadrilaterals complete each proof in your notebook. **These are only a few examples, look at your notes for more!** 1) Determine if quadrilateral PQRS with is a parallelogram.
2) Prove that parallelogram DEFG with is a rhombus. 3) Determine if quadrilateral WXYZ is a rectangle. 4) Prove that parallelogram TJLK is a square.
5) Determine if quadrilateral MATH with is a trapezoid. 6) Determine if rhombus KATE with is a square. 7) Determine if trapezoid MATH with is an isosceles trapezoid.
Name: Date: Period: REVIEW section Directions: Answer each question on the line provided. Show all work in your notebook. 1) The point of concurrency of the three medians is the: (1) centroid (2) circumcenter (3) incenter (4) orthocenter 2) The incenter is formed by connecting the three: (1) medians (2) perpendicular bisectors (3) altitudes (4) angle bisectors 3) The degree measures of the angles of are represented by. Find the value of x. (1) 15 (2) 26 (3) 45 (4) 90 4) In the diagram to the right of parallelogram ABCD with diagonal AC BD, the m<1 = 37 the m<dcb=120. What is the measure of <2? (1) 57 (2) 23 (3) 37 (4) 60 5) In scalene triangle ABC,. What is the order of the sides in length, from longest to shortest? (1) (2) (3) (4) 6) The slope of is the slope of is. If, determine state the value of. 7) In the diagram below, a right circular cone with a radius of 3 inches has a slant height of 5 inches, a right cylinder with a radius of 4 inches has a height of 6 inches. Determine state the number of full cones of water needed to completely full the cylinder with water. 8) In isosceles trapezoid QRST, are bases. If, what is? 9) In the diagram below, line is parallel to line, 10) In the diagram below of isosceles, the line is a transversal. If measure of vertex angle B is. If extends to, what is? point D, what is?