Transcript 4.3 Triangle Inequalities

Warm -up

Copy the pictures, find x and the measure of
each angle.
1.
2.
60
2x
4x
x
X+15
Front reflection: If 2 triangles have all corresponding
angles congruent are the triangles congruent? Explain
4.3 Triangle Inequalities
Year 2 Geometry
Materials:
Patty paper
Ruler & protractor
Chapter 4.3 in your book.
Investigation #1


Follow the directions in the book pg. 214
Use patty paper to trace the lines.
Triangle Inequality Conjecture
The sum of the lengths of the two shorter sides
GREATER THAN
of a triangle must be _______________
the
length of the third side.
Example #1

a.
b.
c.
d.
e.
Determine whether it is possible to draw a
triangle with the given sides. State the
reason.
NO, 2 + 5 < 8
2 cm, 5 cm, 8 cm
YES, 3 + 5 > 7
7 in, 5 in, 3 in
NO, 7 + 13 = 20
20 m, 7 m, 13m
YES, 16 + 30 > 45
16 cm, 30 cm, 45 cm
NO, 9 + 17 < 28
9 km, 17 km, 28 km
Investigation #2
Follow the directions in the book pg. 215
Side-Angle Inequality Conjecture
In a triangle, if one side is longer than another
side, then the angle opposite the longer side
LARGER THAN THE ANGLE OPPOSITE THE SHORTER SIDE
is _________________________________.
Example #2
Arrange the unknown measures in order from
greatest to least.
a.
b.

55°
b
30°
c
f
d
68°
57°
60°
a
e
c, b, a
f, d, e
Example #3
Arrange the unknown measures in order from
greatest to least.
a.
b.
c

87°
a
b
13
c
20
b, a, c
b
61°
18
a
32°
b, c, a
Exterior Angles of a Triangle

Triangle also have exterior angles. If you
extend one side of a triangle beyond its
vertex , then you have constructed an
exterior angle at that vertex.
EXTERIOR ANGLE
REMOTE INTERIOR ANGLES
ADJACENT
INTERIOR
ANGLE
Investigation #3


Follow the directions in the book pg. 215-216
Use patty paper to trace the angles.
Triangle Exterior Angle Conjecture
The measure of an exterior angle of a triangle
IS EQUAL TO THE SUM OF THE MEASURES OF THE REMOTE
____________________________________
INTERIOR ANGLES.
___________________________________.
Example #4

Find the missing value.
a.
b.
135°
x
40°
120°
x
x + 40° = 120°
x = 80°
x + x = 135°
2x = 135°
x = 67.5°
x
Example #5
Find m<E

a.
Find the missing value.
10x+4
b.
4x+5
x+15
68
23x-6°
70°
23x-6 = 68+10x+4
4x+5+x+15 = 70
5x+20=70
5x = 50
X = 10
23x-6=10x+72
13x – 6 = 72
13x = 78
x =6
<E = 10(6) +4 = 64
E
Summary

Write a three complete sentences about three
main ideas from today.
Homework

Pg 216 # 1-16