Slide 1

6.1/6.2 Triangle Inequalities and
Congruence
Learning Objective: to determine if a triangle can be formed
given 3 side lengths, to describe the 3rd side, given 2 sides, and
to identify congruent polygons and their corresponding parts.
B 8 C
2. A student has an average score of
1.
5
5
73 on five tests this semester.
A

14

D

What is the height of
trapezoid ABCD?
A. 2 units
B.3 units
C
C.4 units
D. 6 units

It is later discovered that one
of the tests was graded
incorrectly and the score should
have been 91 instead of 81.
What is the correct average of
the five tests?
A. 74
B. 75
B
C. 76
D. 83


Slide 2

Learning Objective: to determine if a triangle can be formed given 3 side lengths, to
describe the 3rd side, given 2 sides, and to identify congruent polygons and their
corresponding parts

Notes

Triangle Inequality Theorems –
B
A
C

*The sum of the lengths of 2 sides of a
triangle is greater than the length of the 3rd
side.
In  ABC , AB  BC  AC
BC  AC  AB
AB  AC  BC

*One side of a triangle is longer than a 2nd side
if and only if the angle opposite the 1st side is
larger than the angle opposite the 2nd side.


Slide 3

Learning Objective: to determine if a triangle can be formed given 3 side lengths, to
describe the 3rd side, given 2 sides, and to identify congruent polygons and their
corresponding parts

EX 1 – A gardener wants to make a triangular garden. He
has 23 feet of fence with which to form the perimeter of
the garden. Can the gardener make a garden with the
given side lengths?

a. 3 ft, 5 ft, 15 ft?
3  5  15

Can’t be done!

b. 8 ft, 7 ft, 8 ft?

c. 3 ft, 11 ft, 9 ft?

87 8

3  11  9

788

11  9  3

88 7

9  3  11

Shortcut??


Slide 4

Learning Objective: to determine if a triangle can be formed given 3 side lengths, to
describe the 3rd side, given 2 sides, and to identify congruent polygons and their
corresponding parts

EX 2 – In  UVW , UV  8 cm and VW  4 . 3 cm.
a. What do you know about the length of UW ?
UV  VW  UW

VW  UW  UV

UV  UW  VW

8  4 . 3  UW

4 . 3  UW  8

8  UW  4 . 3

12 . 3  UW

UW  3 . 7

UW   3 . 7

Sooo, UW must be between 3.7 and 12.3
b. Sketch 3 possible shapes of  UVW

CKC p. 281


Slide 5

Learning Objective: to determine if a triangle can be formed given 3 side lengths, to
describe the 3rd side, given 2 sides, and to identify congruent polygons and their
corresponding parts

Congruent Polygons – Same size and shape!
A

G

H

*Polygons are congruent iff all
corresponding parts are congruent
B  H
A  O
D   G

B
D

BA  HO
AD  OG
DB  GH

*when naming congruent polygons, list corresponding
angles in order!

  BAD

 H O G


Slide 6

Learning Objective: to determine if a triangle can be formed given 3 side lengths, to
describe the 3rd side, given 2 sides, and to identify congruent polygons and their
corresponding parts

EX 3 – hexagon RTGDFS  hexagon PQMNRE
T
G
7
R
R 120°
(y-55)° P
D
3w+1
100°

S

125° 10

N

F

Find the missing variables
P  R

y  55  120
y  175

M

RN  FD
3 w  1  10

3w  9
w 3

Q


Slide 7

Out – How can you use the names of congruent
polygons to determine the congruent sides?
Summary – I have a
question about…

POW!!

HW – p. 282 #1-19 odd, p. 289 #1-9, 12-15