Download Geometry - Semester 2

Geometry - Semester 2
Mrs. Day-Blattner
2/10/2016
Agenda 2/10/2016
1) Turn in Vocab review sheet
2) Quiz - 8 write in the answers to the questions, 10 multiple
choice - circle on the paper. Show all “work” - reasoning
for ALL questions. 2pts for each part of a question.
3) Lesson 5: How can I fit a quadrilateral in a circle? Stations
ABCD - individual 1st attempts
4) Homework
Circles (lessons 1-4) 8 questions
Show all your work, state the theorem you are using etc.
2 points per part of a question if work shown and it makes
sense. Use extra paper if necessary.
Semester 1 Review 10 questions - select the correct
response from the options given. Circle the answer on the
paper. Show your thinking/work for possible 2 points per
question.
Start Stations Packet when you have turned in the quiz.
New vocabulary
In the first oval for lesson 5
“ Inscribed polygon”
Definition: A polygon is inscribed in a circle if all
the vertices (corners) of the polygon lie on the
circle.
Draw your own example and a non example
(draw a polygon that is NOT inscribed in a circle)
Station A.
Construct a rectangle such that all four
vertices of the rectangle lie on the circle
below.
Given a circle and a rectangle, what must
be true about the rectangle for it to be
possible to inscribe a congruent copy of it
in the circle?
Station A.
Given a circle and a rectangle, what must
be true about the rectangle for it to be
possible to inscribe a congruent copy of it
in the circle? The diagonals of the
rectangle have to be the length of the
diameter of the circle.
Station B.
Construct a kite in the circle below, and
explain the construction using geometry.
https://www.mathsisfun.com/definitions/kite.html
Station C
The figure below shows a rectangle inscribed in a
circle.
a) List the properties of a rectangle.
b) List all the symmetries this diagram
possesses.
c) List the properties of a square.
d) List all the symmetries that a diagram of a
square inscribed in a circle possesses.
Station C
The figure below shows a rectangle inscribed in a
circle.
a) List the properties of a rectangle.
Opposite sides parallel and congruent
four right angles
diagonals congruent and bisect each other
a)Station C
b) List all the symmetries this diagram possesses.
Opposite sides are congruent
all four angles are congruent
diagonals are congruent
figure may be reflected onto itself across the perpendicular
bisector of the sides of the rectangle
-can rotate onto itself with either a 180 degree or 360 degree
rotation, clockwise or counterclockwise
Station C
c) List the properties of a square.
Opposite sides parallel
all sides congruent
four right angles
diagonals congruent, bisect each other, and are
perpendicular
Station C
d) List all the symmetries that a diagram of
square inscribed in a circle possesses.
Same as for rectangle PLUS
all four sides are congruent, figure may be
reflected onto itself across the diagonals, the
figure may be rotated onto itself with either 90
degree or 270 degree rotation, either clockwise
or counter clockwise
Station D
● A rectangle is inscribed into a circle (ABCD). The
rectangle is cut along one of its diagonals and
reflected across that diagonal to form a kite
(ABED). Draw the kite and its diagonal (AE). Find
all the angles in this new diagram, given that the
acute angle between the diagonals of the
rectangle in the original diagram was 40 degrees.
Station D Possible diagram
E
B
A
C
40°
D
Station D cont.
● Given measure of angle ADB = 40 degrees
● then measure angle BDE = 40 degrees
● measure angle BAD = measure angle BED = 90
degrees (BD is a diameter of circle)
● measure angle ABD = measure angle EBD = 50
degrees
● measure angle ABE = 100 degrees
● measure angle ADE = 80 degrees
Station - Challenge!
● With a partner
Homework
Packet of papers with headings: Station A, Station
B, Station C and Station D.
Use your textbook to help - look up the definition of
a kite, remind yourself of all properties of a
rectangle and square. Use pencil.
Problem Set. (page 31 and 32, really difficult to
read, S.19, S. 20 easier) 1- 6 - please write out the
answer for problem 2 on separate lined paper.