Name:________________________________________________
Date:______________________
Period:________
Chapter 11: Coordinate Geometry Proofs
Review Sheet
Complete the entire review sheet (on here, or separate paper as indicated) and hand 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.
__________ (b) All squares are rhombuses.
__________ (c) All parallelograms are rectangles.
__________ (d) A rhombus is a rectangle.
__________ (e) Isosceles trapezoids are trapezoids.
__________ (f) A square is a rectangle.
__________ (g) In a square all sides are congruent.
__________ (h) A rectangle is a square.
__________ (i) Parallel sides of an isosceles trapezoid are congruent.
__________ (j) All quadrilaterals have 4 congruent sides
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
and
(1)
(2)
(3)
What is the length of the segment?
(4
_____ 2) A line segment has endpoints
(1)
(2)
(3)
(4)
and
What are the coordinates of the midpoint?
_____ 3) What is the slope of a line that is perpendicular to the equation is
(1)
(2)
(3)
(4)
_____ 4) In circle O, a diameter has endpoints
(1)
(2)
(3)
and
?
What is the length of the diameter?
(4)
_____ 5) The equation of line k is
. The equation of line m is
(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?
(1)
(2)
(3)
(4)
The lines are:
The coordinates of
_____ 7) What is the equation of a line passing through
(1)
(2)
(3)
and parallel to
(4)
_____ 8) If
(1)
find the coordinates of B.
is the midpoint of
(2)
is
(3)
and
is
(4)
_____ 9) Classify the two lines represented by the equation
(1) parallel
(2) perpendicular
(3) the same
_____ 10) Find the midpoint of the segment joining the points
(1)
(2)
(3)
(4)
and
(4) neither
and
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) and (-6,8), find the distance (in simplest radical form), midpoint, and slope.
2) Given A(6,5) and B(10,6), and C(2,6) and D(4,-2), how are lines AB and 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
6) Given the following pentagon, find:
(a) Perimeter
(b) Area
.
.
and passes through the point (-4,8).
7) Given triangle ABC with vertices A(-3,2), B(-6,5),
and C(-1,4).
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 and BC.
d) How are AB and AC related?
8) Write an equation of the perpendicular bisector of the line segment whose endpoints are (4,8) and (-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
and
is a parallelogram.
2) Prove that parallelogram DEFG with
and
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
and
is a trapezoid.
6) Determine if rhombus KATE with
and
is a square.
7) Determine if trapezoid MATH with
and
is an isosceles trapezoid.
Name:________________________________________________
Date:______________________
REVIEW section
Period:________
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
the value of x.
(1) 15
(2) 26
are represented by
and
(3) 45
. Find
(4) 90
_____ 4) In the diagram to the right of parallelogram ABCD with diagonal AC and BD,
the m<1 = 37 and the m<DCB=120. What is the measure of <2?
(1) 57
(2) 23
(3) 37
(4) 60
_____ 5) In scalene triangle ABC,
length, from longest to shortest?
(1)
(2)
(3)
(4)
and
6) The slope of
is . If
is
and the slope of
. What is the order of the sides in
, determine and 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, and a right
cylinder with a radius of 4 inches has a height of 6 inches. Determine and state the number of full cones of water
needed to completely full the cylinder with water.
8) In isosceles trapezoid QRST,
and
are bases. If
9) In the diagram below, line is parallel to line ,
and line is a transversal. If
and
, what is
?
and
, what is
?
10) In the diagram below of isosceles
, the
measure of vertex angle B is
. If
extends to
point D, what is
?