Download Keys GEO SY13-14 Openers 3-31

Geometry Opener(s) 3/31
3/31
It’s National Clams on the Half Shell Day, Tater
Day, Oranges and Lemons Day, Bunsen Burner
Day, National “She’s Funny That Way” Day and
Cesar Chavez Day!!! Happy Birthday Rhea
Perlman, Al Gore, Christopher Walken, Leo
Buscaglia, Evan ‘Twitter’ Williams, Ewan
McGregor, Arthur Rubinstein, Herb Alpert, Liz
Claiborne, Cesar Chavez, John Fowles, Octavio
Paz, Joseph Haydn and Rene Descartes!!!
3/31
What to do today:
1. Do the opener.
2. Work on Cognitive Tutor.
3. Do the exit pass.
TODAY’S OPENER
Find x so that l || m.
The Last Opener
Agenda
1. Algebra 2 Placement Test (30?)
2. Opener (5)
3. Individual Work 1:  Creation (8)
4. Individual Work 2:  Side Measurement (8)
5. Discussion:  Conclusions (8)
6. Exit Pass (5)
Standard(s)

CCSS-M-G-SRT.5: Use congruence and similarity criteria for
triangles to solve problems and to prove relationships in
geometric figures
Essential Question(s)
 How do I use similarity and congruence to find
numerical relationships among triangle parts?
Objective(s)
 Students will be able to (SWBAT) establish the
congruence or non-congruence of two geometric
figures.
 SWBAT establish the similarity or non-similarity of
two geometric figures.
 SWBAT find missing angle measures using
congruence or similarity.
 SWBAT find missing side measures using
congruence or similarity
Find x so that l || m.
Exit Pass
The Last Exit Pass
HOMEWORK Period 1
No Homework Tonight.
HOMEWORK Period 6
No Homework Tonight.
Extra Credit
Period 1
Period 6
Our Properties So Far…
Name/#
Description
2/11/14
Algebra
Geometry
Segments Angles
Reflexive Property
Symmetric Property
Transitive Property
Addition &
Subtraction
Properties
Multiplication &
Division Properties
Substitution Property
Midpoint Theorem
(2.8)
Segment Addition
Postulate (2.9)
Angle Addition
Postulate (2.11)
Anything equals itself!
Switching preserves
equality!
If the 1st thing = a 2nd, and
that 2nd thing = a 3rd, then
that 1st thing = the 3rd.
If you add or subtract the
SAME thing from equal
things, then the resulting
things are STILL equal.
If you multiply or divide the
SAME thing from equal
things, then the resulting
things are STILL equal.
If 2 things are equal, then
you can replace one with
the other in any equation
or expression.
A midpoint ‘divides’ a
segment into 2 = segments.
For all #s, x = x.
For all #s, if x = y, then
y = x.
For all #s, if x = y and y
= z, then x = z.
For all #s, if x = y, then x
+ z = y + z and x – z = y
– z.
For all #s, if x = y, then x
* z = y * z and x / z = y /
z.
For all #s, if x = y, then,
for example, x + 2 = w
is equivalent to y + 2 =
w.
A point between 2 other
collinear points divides a
segment into 2 parts of a
whole.
A point in the interior of 2
angles divides an angle into
2 parts of a whole.
Supplement Theorem A linear pair is
supplementary.
(2.3)
Theorem 2.6: s supplementary to the same  or to  s are .
Adjacent s with 
Complement
noncommon sides are
Theorem (2.4)
complementary.
Theorem 2.7: s complementary to the same  or to  s are .
Vertical s are .
Vertical Angles
Theorem (2.8)
Distributive Property
If a quantity x is multiplied
by a sum of quantities,
then that quantity x can be
If M is the midpoint of
̅̅̅̅
𝐴𝐵 , then ̅̅̅̅̅
𝐴𝑀  ̅̅̅̅̅
𝑀𝐵.
If M is between A and B,
̅̅̅̅̅ + 𝑀𝐵
̅̅̅̅ .
̅̅̅̅̅  𝐴𝐵
then 𝐴𝑀
If M is in the interior of
DOG, then mDOM +
mMOG = mDOG. (The
converse is ALSO true!)
If A and B form a
linear pair, then they are
supplementary.
If BED and DEN have
 noncommon sides, then
they are complementary.
If 1 and 2 are vertical
s, then they are .
x(a + b) = xa + xb
multiplied by each part of
the sum.
Theorem 2.9:  lines intersect to form 4 right s.
Theorem 2.10: All right s are .
Theorem 2.11:  lines form  adjacent s.
Theorem 2.12: If 2 s are  and supplementary, then each  is a right .
Theorem 2.13: If 2  s form a linear pair, then they are right s.
The sum of the measures of
Angle Sum Theorem
a ’s s is 180°.
(4.1)
If 2 s of 1  are  to 2 s
of a 2nd , then their 3rd s
are .
The m(exterior) of a  =
Exterior Angle
the sum of the m(remote
Theorem (4.3)
interior 1) and m(remote
interior 2).
Corollary 4.1: The acute s of a right  are complementary.
Corollary 4.2: In any , you can’t have more than 1 right  or 1 obtuse .
If 2 sides of a  are
Isosceles Triangle
congruent, then the 2 base
Theorem (4.9)
angles of the  are
congruent.
If 2 angles of a  are
Isosceles Triangle
congruent, then the 2
Theorem Converse
opposite sides of the  are
(4.10)
congruent.
A  is equilateral if and only
Corollary 4.3
if (iff) it is equiangular.
3rd Angle Theorem
(4.2)
Corollary 4.4
Each  of an equilateral 
measures 60°.
mC + mU + mP =
180°.
If C  T and U 
E, then P  A.
mT = mB + mO.
̅̅̅̅  𝐹𝑌
̅̅̅̅, then Angle
If 𝐹𝐿
FLY is congruent to
Angle FYL.
If Angle FLY  Angle FYL,
̅̅̅̅  𝐹𝑌
̅̅̅̅
then 𝐹𝐿
If C  O  W, then
COW is equilateral. If
̅̅̅̅  ̅̅̅̅̅
𝐶𝑂
𝑂𝑊  ̅̅̅̅̅
𝑊𝐶 , then
COW is equiangular.
The mC = mO =
mW = 60°.
Notes: Parallel Postulates
1
3-21
2
3
4
5
6
7
CO s
|| lines
Postulate
AE s
|| lines
Postulate
CI s
|| lines
Postulate
AI s
|| lines
Postulate
 lines
|| lines
Postulate
Parallel
Postulate
8
If corresponding s are , then lines are ||.
If alternate exterior s are , then lines are ||.
If consecutive interior s are supplementary, then lines
are ||.
If alternate interior s are , then lines are ||.
If 2 lines are  to the same line, then lines are ||.
You are given a line and a point not on the line. There is
ONLY ONE line through that point that’s || to the given
line.