Download Keys GEO SY13-14 Openers 2-18

Geometry Opener(s) 2/18
2/18
It’s Thumb Appreciation Day, Pluto Day and
National Crab-Stuffed Flounder Day!!! Happy
Birthday Regina Spektor, Jillian Michaels, Molly
Ringwald, Dr. Dre, Matt Dillon, Greta Scacchi,
Vanna White, Cybill Shepherd, Yoko Ono, Toni
Morrison, Helen Gurley Brown, George Kennedy,
Jack Palance, Louis C. Tiffany and Mary 1st of
England!!!
2/18
What to do today:
1. Do the opener.
2. Check your HW.
3. Take some thm./post./cor. notes.
4. Record a proof model.
5. Write 2 proofs.
6. Ask ?s about/work on yesterday’s HW.
7. Do the exit pass.
TODAY’S OPENER
Agenda
1. Opener (5)
2. (P1) HW Check: Text ?s, p. 118, #30-37, #39-44,
#47-52, #55-57 (10)
3. (P6) HW Check: Text ?s, p. 98, #20-25 and p. 104,
#4-6 & #12-18 (10)
4. Lecture: Some additional laws (15)
5. Model: Proving the Exterior  Theorem (5)
6. CW: Text ?s, p. 190, #39-40 (10)
7. HW ?s and time (5?)
8. Exit Pass (5)
Standard(s)
 CCSS-M-G.CO.10: Prove theorems about
triangles.
Essential Question(s)
 How do I prove a conditional conclusion is true?
Objective(s)
 Students will be able to (SWBAT) identify a
conclusion.
 SWBAT identify one or more hypotheses (givens).
 SWBAT transform a hypothesis/hypotheses into a
conclusion through a series of steps.
 SWBAT attach a justifying reason to each step.
1. (P6) Write the statement then state the
property that justifies it.
a. If DE = FG, then FG = DE.
b. If XY = WZ, then XY + TU = WZ + TU.
c. If m1 + m2 = 180 and m2 + m3 =
180, then m1 = m3.
d. If 1 and 2 are vertical angles, then
m1 = m2.
2. (P1) If y = 4x + 9 and x = 2, then y = 17.
Show that the conclusion is true by solving
the equation step by step and identifying
what property or theorem allows you to
perform that step.
The Last Opener
1. (P1) Write the statement then state the property
that justifies it.
a. If DE = FG, then FG = DE.
b. If XY = WZ, then XY + TU = WZ + TU.
c. If m1 + m2 = 180 and m2 + m3 =
180, then m1 = m3.
d. If 1 and 2 are vertical angles, then
m1 = m2.
2. (P6) Give me an example of the Distributive
Property...before and after. Then, in words,
explain what the distributive property does.
Exit Pass
If mABD = 44 and mABC = 98 and D is in the interior of ABC, find mDBC.
Show all your steps and identify the properties you used to advance from one
step to another. Start with “Statement: D is in the interior of ABC Reason:
Given”.
Answer?
The Last Exit Pass
Write a conditional that is logically equivalent to its inverse.
Answer?
HOMEWORK Period 1
Finish  Congruence Wkshts.
HOMEWORK Period 6
Finish  Congruence Wkshts.
Extra Credit
Period 1
Period 6
Stephanie C. (3x)
Prisma
Ayelen (4x)
Saul (4x)
Alejandra (4x)
Magda
Stephanie M. (4x)
Tanya (2x)
Crystal
Demina (2x)
Marisol
Sergio (7x)
Jesus (7x)
Cynthia (3x)
Jocelyn (6x)
Carolina (2x)
Melanie B. (4x)
Melanie G.
Maria
Lily (3x)
Denise
Imelda
Valerie
Our Properties So Far…
Name/#
Description
2/11/14
Algebra
Geometry
Segments
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.
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.
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.
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)
Angles
̅̅̅̅ ,
If M is the midpoint of 𝐴𝐵
̅̅̅̅̅  𝑀𝐵
̅̅̅̅̅.
then 𝐴𝑀
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 .
If a quantity x is
multiplied by a sum of
quantities, then that
quantity x can be
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
Angle Sum Theorem
of a ’s s is 180°.
(4.1)
Distributive Property
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
Theorem (4.3)
m(remote 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 .
3rd Angle Theorem
(4.2)
x(a + b) = xa + xb
mC + mU + mP =
180°.
If C  T and U 
E, then P  A.
mT = mB + mO.