3.1
Name (print first and last) _____________________________________ Per_____ Date: 10/4 due 10/7
3.1 Assumptions and Circle Symmetry
Geometry Regents 2013-2014 Ms. Lomac
SLO: I can use the basic assumptions to justify observations of reflection symmetry in circles
(1)  Draw: Acute angle TRW congruent to angle ERW
(2)  Geometry Assumptions 1-8 (see handout) Add diagrams to help you remember each assumption.
(3)  Use the circle on the back of this paper. You will need to fold this paper. That is fine. 
 (a) Find point A and fold the circle so that point A coincides with A'. Crease the fold.
 (b) With your pencil, trace the crease from one edge of the circle to the other.
 (c) Repeat steps a and b for each pair of points on the circle (B & B', C & C', and D & D') .
 (d) Look at the lines that are formed by the creases. All of the creases pass through the _______________ of the
circle. Because they pass through the _______________ of the circle, the segments are
______________________ of the circle. All of the segments are also lines of symmetry because the half
circles are reflections of one another. How many lines of symmetry does a circle have?_____________
(5)  Obtain a circle symmetry page.
 (a) Find the circle with A and A'. Fold the circle so that A coincides with A’ and crease the fold.
 (b) Trace the crease with a pencil and label the points of intersection with the circle T and W.
 (c) Use a straightedge to connect point A to A'.
 (d) Find the point where the two segments intersect and label it X.
 (d) Repeat steps (a) through (c) for the other circles on the page.
 (e) Because points A and A' are __________________ of each other, the crease is a line of ___________________.
The crease is also the __________________ of the circle. The relationship between AX and A' X is that they
are ____________________. Therefore, TW ___________________ AA' . ∠AXA' is a
____________________ angle which measures _____. Since ∠A'XT is a reflection of _______, the measure of
∠A’XT is ______. For any reflection, the segment connecting a preimage point to its image point is
___________________ to the line of____________________. (Also called the line of __________________)
SAVE THE CIRCLE SYMMETRY PAGE. YOU WILL NEED IT FOR ACTIVITY 2.
3.1
D'
A
B'
B
A'
D
C
C'
3.1
Circle Symmetry Page (3.1)
A
A'
B
B'
C'
C
D
D'
3.1 HW
Name (print first and last) _____________________________________ Per_____ Date: 10/4 due 10/7
3.1 HW Assumptions and Circle Symmetry
Geometry Regents 2013-2014 Ms. Lomac
(1) Construct the perpendicular bisector of segment AB. Clearly label the points you use to complete the construction with
the letters C and D.
A
B
(2) Complete the explanation below that describes how the perpendicular bisector of AB is supported by the work we did
in class today.
The construction of the perpendicular bisector of AB is supported by the work we did in class today because point _____
Is a reflection of point_____which means__________________________________________________________________
_______________________________________________________________________________________________
ASSUMPTION 1: Basic rigid motions preserve the shape and measures of a figure.
ASSUMPTION 2: Two triangles with congruent sets of segments are congruent.
Geometry Assumptions
0! Line
0@ Plane Separation
2 distinct points determine exactly 1 line.
Given a line contained in the plane, the points of the plane that do not lie on the
line form two sets called half planes such that:
(a) If 2 points are in one half plane, the segment between them is on the half
plane
(b) If point P is in one half plane and Q in the other, then PQ intersects the edge
of the half plane.
0# Distance
For every pair of points A and B, there is a corresponding distance from A to B.
0$ Ruler
Every line has a coordinate system.
0% Plane
3 noncollinear points determine exactly 1 plane.
0^ Basic Rigid Motions
(a) map preimages to images (points to points, lines to lines, line segments
to line segments, and rays to rays).
(b) preserve measurements (distance, angles).
0& Protractor
Angle Addition
0* Parallel Postulate
(a) For every angle (∠AOE) there is a corresponding measure of rotation (m∠AOE)

(b) Let OE be a ray on the edge of the half-plane H. For every angle measure r

such that r is between 0° and 180° there is exactly one ray OE with E in the half
plane H such that m∠AOE equals the measure r.
NOTE: In this course, reference to any angle with 3 letters will refer to angles with
measures greater than zero and less than or equal to 180° unless otherwise
specified.
(c) If C is a point in the interior of ∠AOE then m∠AOC + m∠COE = m∠AOE.
(d) If two angles form a linear pair, then they are supplementary.
Given a line and a point not on the line, there is at most one line that passes
through the point that is parallel to the given line.
The Power of Circles
(a) ________________________________________________________________
________________________________________________________________
________________________________________________________________
(b) ________________________________________________________________
________________________________________________________________
________________________________________________________________
3.1 Exit Ticket
Name_________________________________________Per______
Complete the statement. You may use diagrams to support your statement.
Circles have _________ lines of symmetry because
____________________________________________________________________
____________________________________________________________________
__________________________________________________________________________________________________
3.1 Exit Ticket
Name_________________________________________Per______
Complete the statement. You may use diagrams to support your statement.
Circles have _________ lines of symmetry because
____________________________________________________________________
____________________________________________________________________
__________________________________________________________________________________________________
3.1 Exit Ticket
Name_________________________________________Per______
Complete the statement. You may use diagrams to support your statement.
Circles have _________ lines of symmetry because
____________________________________________________________________
____________________________________________________________________
__________________________________________________________________________________________________
3.1 Exit Ticket
Name_________________________________________Per______
Complete the statement. You may use diagrams to support your statement.
Circles have _________ lines of symmetry because
____________________________________________________________________
____________________________________________________________________
__________________________________________________________________________________________________