# Inequalities in Triangles

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```					Inequalities in
Triangles
One or two?

DAY 2
Inequalities in Triangles
• Let’s do a discovery!

• Materials: protractor, straight-edge

• 1. Draw a scalene triangle. Label it ABC.

• 2. Measure each side in cm and each
angle in degrees. Mark this measures
into the triangle.
Inequalities in Triangles
• 3. Complete the following chart:
Large   Large   Med     Med    Small   Small
angle   side    angle   side   angle   side

• What conclusion can be made?
• (This is not a profound answer.)
Inequalities in Triangles
• Let’s work with ONE triangle first…

• If one angle of a triangle is
larger than a second angle,
• then the side opposite the first
angle is longer than the side
opposite the second angle.
Inequalities in Triangles
• Yes, it is just that
straight forward.
B

• Name the largest
to smallest angle.         9

11

A  C  B          A

6
C
Inequalities in Triangles
• Name the largest
B
to smallest side.

• Remember you can
only work in ONE
triangle at a time.      A   80
60       40
C
D

BC  DC  BD  AB  AD
Discovery 2
• Using triangle from Discovery 1,
• Complete the following:
lm s

•   lsm       The sum of two sides of a
•                triangle is _____________
•   m s  l     the third.
•                              greater than
Inequalities in Triangles
• End of day one!

• Homework:
– Page 14 top #9 – 15
– Page 12 skip #14 - 17
Inequalities in Triangles
• Day Two!
• Let’s do a discovery:
• Materials: Compass, rubber band, straight-edge

• 1. Draw two non-congruent segment AB
and BC so that you create an acute
angle whose vertex is B.
Measure length AB and redraw it with a dotted line
forming an obtuse angle whose vertex is B.

• 2. Place band on the ends of the
compass. And set the ends on point A
and C.
Inequalities in Triangles
• 3. Now stretch the width of the
compass. Keep the same length for AB
and BC.

• 4. What happens to angle B?

• 5. What happens to segment AC?

• 6. What is true about segment AB ad BC?
Inequalities in Triangles
• Discuss with your group:

• When comparing one triangle to
another, what is true about the
changing angle and side?
Inequalities in Triangles
• These theorems are just fun to read!

• If two sides of one triangle are congruent
to two sides of another triangle and the
included angle of the first is larger then
the included angle of the second, then the
third side of the first is larger then the
third side of the second triangle.
Inequalities in Triangles
• What does that
B
mean?                                   E

• Which must be                    D 60

• the bigger side?   A   100

F
C
Inequalities in Triangles
• How about this one?

• If two sides of one triangle are
congruent to two sides of another
triangle and the third side of the first
is larger then the third side of the
second, then the included angle of
the first is larger then the included
angle of the second triangle.
Inequalities in Triangles
• What does that           B
E
mean?

D
• Which must be           100
60
A
• the bigger angle?

F
C
Inequalities in Triangles
• Homework:
• Page 13
• Page 14 finish
• Page 15

```
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