Download Geometry/Trig Name: Relationships in Triangles GSP Lab

Geometry/Trig
Relationships in Triangles GSP Lab - Answers
Name: __________________________
Date: ___________________________
Scalene Triangle – A triangle with no congruent sides.
Sketch a picture of the
scalene triangle that you
created in Sketchpad. Fill in
all angle measurements and
segment lengths.
Are any of the angle measures the same? No
Which side is longest? ___________________________________
Which angle is largest? __________________________________
Which side is shortest? _________________________________
Which angle is smallest? _________________________________
What is the relationship between the position of the longest side and the
Scalene Triangle
largest angle? They are across from one another.
What is the relationship between the position of the shortest side and
the smallest angle? They are across from one another.
Ex1 – List the angle measurements
in order from smallest to largest.
Ex2 – List the side lengths in
order from shortest to longest.
(Diagram NOT drawn to scale!)
(Diagram NOT drawn to scale!)
K
Q
12cm
5cm
32 °
R
J
14cm
85 °
63 °
P
L
L, J, K
RP, RQ, QP
Go to my website and find Unit 3 to check your examples. When you are ready to take the check for
understanding quiz called “Scalene Triangle” through Quia.
Isosceles Triangle – A triangle with two congruent sides.
Turn to page 134 of a textbook. Read the paragraph under the heading 4-4
The Isosceles Triangle Theorems and complete the first four lines of the
fill in notes below:
The congruent sides of the Isosceles Triangle are called the legs.
The third side is called the base.
The two angles across from the legs are called the base angles.
The angle across from the base is called the vertex angle.
Which angles are the base angles in your sketch? A and C
What is interesting about the measures of the base angles? They are
congruent.
Try to complete the following Theorem:
The base angles of an isosceles triangle are congruent.
Don’t worry, we’ll prove this theorem during unit 4. 
Go to my website and find Unit 3 to check your examples. When you are ready to take the check for
understanding quiz called “Isosceles Triangle” through Quia.
Isosceles Triangle
p. 134 of book
Sketch a picture of the
isosceles triangle provided
for you in Sketchpad. Fill
in all angle measurements
and segment lengths.
Geometry/Trig
Relationships in Triangles GSP Lab - Answers
Name: __________________________
Date: ___________________________
Equilateral Triangle – A triangle with three congruent sides.
What is true about all three side lengths? All three sides have equal
lengths.
Sketch a picture of the
equilateral triangle that
you created in Sketchpad.
Fill in all angle
measurements and
segment lengths.
What is true about all three angle measures? All three angle
measures are equal. They are all 60 degrees.
Equilateral Triangle
Corollary 1 (p. 135): An equilateral triangles is also equiangular.
Corollary 2 (p. 135): An equilateral triangle has three 60 degree
angles.
Example 3:
A
5x + 2
B
mB = 60
60°
10x - 14
5x + 2 = 10x – 14
16 = 5x
x = 16/5 = 3.2
C
mC = 60
x = 16/5 = 3.2
AB = 5(16/5) + 2 = 18
AC = 18
BC = 10(16/5) – 14 = 18
Go to my website and find Unit 3 to check your examples. When you are ready to take the check for
understanding quiz called “Equilateral Triangle” through Quia.
Diagrams for Quia Quizzes (Diagrams are NOT drawn to scale):
Diagram 1
A
Diagram 2
J
60°
4in
B
80°
40°
M
Diagram 3
100°
40°
N
C
K
Diagram 4
10in
L
12in
S
Q
18in
12in
R
12in
P