Download Calculus Fall 2010 Lesson 01

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Lesson Plan #003
Date: Wednesday September 14th, 2016
Class: Geometry
Topic: Definitions involving angles
Aim: What are some definitions involving angles?
Objectives:
1) Students will be able to state various angle properties.
NOTE: Bring your compass, straight-edge, protractor, & calculator to class every day.
HW# 003:
Do Now:
PROCEDURE:
Write the Aim and Do Now
Get students working!
Take attendance
Go over the Do Now
Is this person hitting the ball at the correct angle? Hmm…, let’s first
discuss angles and their properties.
Definition: An angle is the set of points that is the union of two rays
having the same endpoint.
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The two rays are called the sides of the angles, and their common endpoint is called the vertex of the angle. The sides of the angle
shown are
BA and BC . The vertex is point B.
How can we name the angle to the right?
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Name all the angles shown at right.
How do we determine how big is an angle?
What is a unit of measurement of an angle?
What can be used to measure an angle?
Find the measure of <2. ____________
Angles can be classified according to their measures?
Definition: A right angle is an angle whose degree measure is 90o.
Definition: A straight angle is an angle whose degree measure is 180o.
Type of Angle
Description
Acute Angle
an angle that is less than 90°
Obtuse Angle
an angle that is greater than 90° but less than 180°
Reflex Angle
an angle that is greater than 180°
Ganiometer: In physical therapy and occupational therapy, a goniometer is an instrument which measures range
of motion joint angles of the body
The patient at the right had a torn meniscus and to alleviate
the pain, she had a partial meniscectomy of the left knee.
After the partial meniscectomy, the patient had limited range
of motion. After six weeks of physical therapy, knee
flexion was measured using a goniometer. How many
degrees of range of motion does she have?
To determine if she has returned to normal range of motion, knee flexion is measured for her right knee and the degree measure of
the range of motion is the same as the left leg. What can we say about the two degree measures?
What is the definition of congruent angles?
What can you conclude about
S and G ? _______________
What markings indicate congruent angles?
__________________
Why are the 2 angles below congruent?
What can you conclude about
C and C ' ?
Construct an angle congruent to a given angle. http://www.mathopenref.com/constcopyangle.html
1. To draw an angle congruent to A, begin by drawing a
ray with endpoint D.
2. Place the compass on point A and draw an arc across
both sides of the angle. Without changing the compass
radius, place the compass on point D and draw a long arc
crossing the ray. Label the three intersection points as
shown.
3. Set the compass so that its radius is BC. Place the
compass on point E and draw an arc intersecting the one
drawn in the previous step. Label the intersection point F.
4. Use the straightedge to draw ray DF.
EDF BAC
Assignment #1: Construct an angle congruent to the angle below.
Assignment #2: Construct an angle that is twice the
size of the above angle.
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Definition: Adjacent Angles are two angles in a plane that have a common vertex and a common side, but no common interior
points.
Definition: A bisector of an angle is a ray whose endpoint is the vertex of the angle, and that divides the angle into two congruent
angles.
Given the diagram at right and
be made?
BD bisects  ABC , what statements of congruence can
What statements of equality can be made?
http://www.mathopenref.com/constbisectangle.html
Bisect Angle. To construct the Angle Bisector of an angle, follow the following steps.
Given. An angle to bisect. For this example, angle ABC.
Step 1. Draw an arc that is centered at the vertex of the angle. This arc can have a radius of any length.
However, it must intersect both sides of the angle. We will call these intersection points P and Q This
provides a point on each line that is an equal distance from the vertex of the angle.
Step 2. Draw two more arcs. The first arc must be centered on one of the two points P or Q. It can
have any length radius. The second arc must be centered on whichever point (P or Q) you did NOT
choose for the first arc. The radius for the second arc MUST be the same as the first arc. Make sure
you make the arcs long enough so that these two arcs intersect in at least one point. We will call this
intersection point X. Every intersection point between these arcs (there can be at most 2) will lie on
the angle bisector.
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Step 3. Draw a line that contains both the vertex and X. Since the intersection points and the vertex all
lie on the angle bisector, we know that the line which passes through these points must be the angle
bisector.
Assignment #1: Construct the angle bisector of the angle at right.
Assignment #2: Construct an angle that is 1.5 times the above angle.
Group Work:
The above observation leads us to the Angle Addition postulate. Also known as the partition postulate, the whole is equal to the
sum of its parts.
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