Download 28 Aug 2015 9:50 - 11:20 Geometry Agenda

28 Aug 2015 9:50 - 11:20
Geometry Agenda
1st 10 minutes - corrections on Quiz - looking for
all correct use of geometry notation
Station Reports - Station 1
Vertical Angles
Homework
In Geometry some things can
be assumed to be true and
some things can be proven.
Most things that we assume to
be true are known as
postulates.
Most things that are proven
true are known as theorems.
We are going to use a postulate to prove
something on this page. So let’s start with
a postulate (something we assume to be
true.)
Postulate: Two adjacent
angles (angles that share a
side and vertex) that form a
straight angle have a sum of
180°.
a°
b°
c°
1) What can we say about the sum of angles a
and b?
a°+ b° =
a°
b°
c°
1) What can we say about the sum of angles a
and b?
a°+ b° = 180° and
b° + c° =
a°
b°
c°
1) What can we say about the sum of angles a
and b?
a°+ b° = 180° and
b° + c° = 180°
a°
b°
c°
2) What can we say about the relationship
between (a°+ b°) and (b° + c°) ?
a°
b°
c°
2) What can we say about the relationship
between (a°+ b°) and (b° + c°) ?
(a°+ b°) = (b° + c°)
a°
b°
c°
3) Looking at your answers to #1 and #2, explain
below how you know that a° = c°.
Since
a°+ b° = b° + c°
We can then subtract b° from each side of the
equation so
a°+ b° - b° = b° + c° - b°
a°
b°
c°
3) Looking at your answers to #1 and #2, explain
below how you know that a° = c°.
Since
a°+ b° = b° + c°
a°+ b° - b° = b° + c° - b°
Which simplifies to
a° = c° or a = c
Theorem: Vertical Angles are
Congruent
a°
b°
c°
Vertical angles - two nonadjacent angles formed
by intersecting lines
Theorem: Vertical Angles are
Congruent
m∠ABC = m∠EBD
C
A
B
E
∠ABC
D
∠EBD
Parallel lines and Transversals
For the picture below we are going to assume that
line p and line q are parallel. Line t is a
transversal.
For all of the questions on this page, we are going
to assume the fact below. This is one of the basic
geometry postulates. (Things we assume to be
true.)
Postulate: If two parallel lines are cut
by a transversal, then corresponding
angles are congruent.
In this case, this means e° = h°
1. If we know the e° = h° by the postulate
above, what can we say about the
relationship between f° and h° ?
On the previous page we stated that vertical
angles are congruent. In this example f°=e°,
these are a pair of vertical angles.
We also know that e°= h°,
Therefore we can state that f° = h°.
2. Using the postulate above and our
conclusion in #1, what can we say
about the relationship between g° and
h°? Explain how we know.
e° + g°= 180°, these are supplementary angles
Since we also know that e°= h°, we can
substitute h° into the equation to get
h° + g° = 180°.
So h and g are also supplementary angles.
1. If two parallel lines are cut by a
transversal, then alternate interior
angles are congruent.
2. If two parallel lines are cut by a
transversal, then same-side interior
angles are supplementary.
Equations and Transversals
Each figure consists of two parallel lines and a
transversal. Find the values of x and y. Show
reasoning.
Same side interior
angles are
1.
supplementary
128°
2x°
Equations and Transversals
Each figure consists of two parallel lines and a
transversal. Find the values of x and y. Show
reasoning.
Same side interior
angles are
1. 128° + 2x° = 180°
supplementary
128°
2x°
Equations and Transversals
Each figure consists of two parallel lines and a
transversal. Find the values of x and y. Show
reasoning.
Same side interior
angles are
1. 128° + 2x° = 180°
supplementary
128°
2x° = 180°- 128°
2x°
x° = 52°
2
x = 26°
Equations and Transversals
Each figure consists of two parallel lines and a
transversal. Find the values of x and y. Show
reasoning.
Complete 2, 3, 4, 5, and 6.
Homework - Vertical Angles
Chapter 2, page 130 - 131
Questions 8, 9, 10, 11, 12, 13, and 28.
Use paper put into your binder after the
Equations and Transversals page.
Draw the diagram each time. Show your
reasoning.