Download 4 - Garnet Valley School District

Geometry A Unit 4 Day 1
4.1 Triangles and Angles
I. Warm-Up / Introduction
A. Vocabulary
WORD BANK
Acute Triangle
Isosceles Triangle
.
Equiangular Triangle
Scalene Triangle
Equilateral Triangle
Obtuse Triangle,
Right Triangle
Fill in the blank with the word from the WORD BANK that matches the definition.
1. _______________________ - A triangle with 2 or more equal sides.
2. _______________________ - A triangle with 3 equal sides.
3. _______________________ - A triangle with no equal sides.
4. ___________________ - A triangle with one 90 angle.
5. ___________________ - A triangle with one angle measuring more than 90 .
6. ___________________ - A triangle with all angles measuring less than 90 .
7. ___________________ - A triangle that has three angles with the same measure.
One thing to be aware of, every EQUILATERAL TRIANGLE is an ISOSCELES
TRIANGLE…
Explain: _____________________________________________________________
____________________________________________________________________
____________________________________________________________________
…but not every ISOSCELES TRIANGLE is an EQUILATERAL TRIANGLE
It’s just that calling an equilateral triangle an isosceles one is not being as specific as
possible.
B. Proof of a Property You Probably Knew
4 1
5
Given: AB | | CD
Prove:  1 +  2 +  3 = 180o.
Statement
Reason
2
1. ________________________
1. ____________________


 180
2. ________________________
2. Linear Trio/Definition of Straight Angle
3. _________________________
3. ___________________
4. ________________________
4. ___________________
5. ________________________
5. _____________________
The very useful result of the proof above is the “Triangle Sum” Theorem
(Interior) Triangle Sum – The three (interior) angles of any triangle add to 180o.
This sets up a second thing to be aware of. Every EQUIANGULAR TRIANGLE is an
ACUTE TRIANGLE…
Explain: _____________________________________________________________
____________________________________________________________________
____________________________________________________________________
…but not every ACUTE TRIANGLE is an EQUIANGULAR TRIANGLE
It’s just that calling an equiangular triangle an acute one is not being as specific as
possible.
3
Applications of Definitions and Theorem
Problem Set #1.
Classify each of the following. Use at least one word from each list.
List A: Equilateral, Isosceles and Scalene
Ex. 1:
List B: Acute, Obtuse, Right and Equiangular
Ex. 2:
59
30
________________________ and
_________________________ and
_______________________
_________________________
60
Ex. 3:
60
________________________ and
_______________________
Ex. 4: Find x and determine if  ABC is right
acute or obtuse and whether it is scalene
equilateral or isosceles.
 A = 3x  40
 B = x
 C = 3x 10
____________________________
____________________________
C. A Second Round of Vocabulary
N
Below, the definitions of Legs and Hypotenuse are given.
Name the legs and the hypotenuse in the right triangle drawn.
L
M
1. Leg – A side of a right  that helps form the right  . ______ and _______
2. Hypotenuse – The side of the right  across from the right  . _________
D
D. Parts of and Isosceles Triangle
Below, the definitions of Base, Base Angle, Legs and Vertex Angle
are given. Name each in the isosceles triangles drawn.
1.
Leg - One of the sides of equal length. ______ and ______
2. Base - The side that connects the legs. ________
E
F
E
3. Vertex Angle - The angle included between the
legs of an isosceles triangle.  ____________
D
4. Base Angle - One of the angles included between the base and one of the legs.
 _____ and  ______
One thing to consider about the two different meanings of the word “legs”. In an
isosceles right triangle, is there any concern that the legs (two sides that make the right
angle) would not be the legs (the two sides that are equal).
YES or NO ? Explain. _________________________________________________
_______________________________________________________________________
_______________________________________________________________________
F