Geometry Lesson Plan Section 4.1 Triangles and Angles

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Oct 10, 2013 (4 years and 1 month ago)

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Geometry
Lesson Plan

Section
4
.1
Triangles and Angles






1.

Objectives
: SWBAT





o

Identify attributes of triangles
.

o

Classify
tri
angles
by sides and angles

o

Apply the Triangle Sum and Exterior Angle theorems






2.

Vocabulary
:



Set 1:

adjacent sides,

vertices
, interior angle, exterior angle, vertices



Set
2
:

equilateral ▲,

scalene

▲,

isosceles ▲, base, base angles





Set
3
:

acute ▲, obtuse ▲,

right ▲, equiangular ▲
, hypotenuse,

leg



3
.
Theorems
:




4.1

Triangle Sum Theorem.
The sum of the interior angles in a triangle is 180
°
.


4.2 E
xterior Angle Theorem
.

The measure of an exterior is equal t
o

the sum of the two


remote

interior angles.




4
.
Instruction


a) Vocabulary
S
et

A






A


ABC







Vertices
: A, B, and C

Sid
es:
AB, BC, and CA


B

C


Adjacent sides

have a common vertex.

Opposite side
:

Across from the vertex: AB is opposite to C.


Interior angles:

3,

5, and

6

Exterior angles:

1,

2,

4, and

7



R









1 2










3







4 5 6
S







T

7






Note:

When we say

A, it means the interior angle at A
;

3






b) Vocabulary
Sets B and C




Classify by Sides


Equilateral Triangle


Isosceles Triangle


Scalene triangle

3 congruent sides


2 congruent sides


No congruent sides









Classify by Angles


Acute Triangle


Equia
ngular

Triangle


Right Triangle


Obtuse Triangl
e

3 acute angles


3 congruent angles


1 right angle


1 obtuse angle













c) Special Sides and Angles





Right Triangles



Isosceles Triangle

















hypotenuse

leg



leg

base




















leg


leg











Example
:












X














2

Classify
▲XYZ. _________ __________

Name the
base
(s). ______





1 3 4 5

Name the
leg
(s). _______

Name the
interior angles
. ________




Y





Z

Name the
exterior angles
. ________





d) Theorems about Angl
e Measurement


Triangle Sum Theorem.

The sum of the interior angles in a triangle is 180
°
.

For all triangles






1.





2.


A




B



45° x










30°








32°

75° x



C



m

A +
m

B +
m

C = 180°




Exterior Angle Theorem
.


The measure of an exterior is equal to the sum of the two remote interior angles.


For all triangles




1


2 3 4


m

1 =
m

3 +
m

5



5




m

4 =
m

2 +
m

5


6








m

6 =
m

2 +
m

3




Examples




52°


98° 30° 153° x°









111°


55°


x° y°


67°



50° 82°


75° x° y° z°







5
.

Assessment:


Questioning and Discussion of homework problems the following day.



6
.
Homework:

Pg. 198; 1


30

Geometry Lesson Plan

Section 4.1
Triangles and Angles

(Day 2)





1.

Objective
:
Solve problem
s using the Triangle Sum and Exterior Angle theorems



Triangle Sum Theorem.



Exterior Angle Theorem
.


The sum of the interior angles is 180
°
.

The measure of an exterior is equal to the


sum of the two remote interior angles.


A






R






B


C U S T



m

A +

m

B +
m

C = 180°



m

USR =

m

R +
m

T



2. Examples:


Solve for “x”

1.






2.




9x + 10 10x


4











15x + 2


7x


11 5x + 12


















7x + 124




3.
Given

▲ABC.





4.

Write an
equation of a line with a









slope of ½ and through (6,
-
5).


a) Solve for “x”


b) Find the measurement of each angle


c) Classify the triangle


m

A = x°

m

C = 2x°

m

C = (2x + 7)°




5.

Assessmen
t:


Questioning and Discussion of homework problems the following day.



6.
Homework:

Pg. 199; 31


39, 47, 61


65

Study Guide: Section 4.1
Triangles and Angles


Notation: ▲ABC

A







Vertices
: A, B, and C

Sides:
AB, BC, and CA


B

C


Adjacent sides

have a common vertex.

Opposite sides
:

Across from the vertex:

AB is opposite to

C.


Interior angles: ________
____________ Exterior angles:_____________________________



Classify by Sides

___________________

___________________

________________________

3 congruent sides


2 congruent sides


No congruent sides







Classify by Angles

_____________

___
______________


______________

________________

3 acute angles


3 congruent angles


1 right angle


1 obtuse angle









1.











X














2

Classify
▲XYZ. _________ __________

Name the
base
(s). ______





1

3 4 5

Name the
leg
(s). _______

Name the
interior angles
. ________




Y





Z

Name the
exterior angles
. ________


Triangle Sum Theorem.



Exterior Angle Theorem
.


The sum of the interior angles is 180
°
.

The mea
sure of an exterior is equal to the


sum of the two remote interior angles.



A






R






B C U

S T V



m

A +

m

B +
m

C = 180°



m

USR =

m

R +
m

T


Warm up 10/16/07


Find “x” and “y”


1.





y



42°










x











51°