MA.912.G.4.7: Apply the inequality theorems: triangle inequality, inequality in one triangle, and the Hinge Theorem.

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Geometry Mini-Lesson
Which of the following statements regarding the
figure at left is true?

1. AB is the longest side of ?ABC.
2. AC is the longest side of ?ABC.
3. BC is the shortest side of ?ABC.
4. AB is the shortest side of ?ABC.

MA.912.G.4.7 Apply the inequality theorems
triangle inequality, inequality in one triangle,
and the Hinge Theorem.
3
Geometry Mini-Lesson
MA.912.G.4.7 Apply the inequality theorems
triangle inequality, inequality in one triangle,
and the Hinge Theorem.
4
Geometry Mini-Lesson
MA.912.G.4.7 Apply the inequality theorems
triangle inequality, inequality in one triangle,
and the Hinge Theorem.
5
Geometry Mini-Lesson
Alex is playing tetherball and notices that when
he hits the ball with more force, it swings in a
wider arc. Considering that ABAB and ACAC in
the figures below, what can Alex conclude about
playing tetherball?

1. BC is longer when Alex hits the ball with less
   force.
2. Angle A is greater when Alex hits the ball with
   less force.
3. Angle A is greater when Alex hits the ball with
   more force.
4. BC is the same length whether Alex hits the ball
   with more or less force.

MA.912.G.4.7 Apply the inequality theorems
triangle inequality, inequality in one triangle,
and the Hinge Theorem.
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Geometry Mini-Lesson
Given the figure at right, which of the following
could be the length of AB ?

1. 9
2. 11
3. 15
4. 19

MA.912.G.4.7 Apply the inequality theorems
triangle inequality, inequality in one triangle,
and the Hinge Theorem.
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Geometry Mini-Lesson
Given the figure below, which of the following is
true?

1. AD gt AB
2. BD gt BC
3. DC gt AB
4. AB gt DC

MA.912.G.4.7 Apply the inequality theorems
triangle inequality, inequality in one triangle,
and the Hinge Theorem.
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Geometry Mini-Lesson
Which of the following lists the angles from
least to greatest in measurement?

1. A, B, C
2. C, B, A
3. B, C, A
4. A, C, B

MA.912.G.4.7 Apply the inequality theorems
triangle inequality, inequality in one triangle,
and the Hinge Theorem.
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Geometry Mini-Lesson
Which of the following statements regarding the
figure is true?

1. XZ is the longest side of ?XYZ.
2. YZ is the longest side of ?XYZ.
3. XY is the shortest side of ?XYZ.
4. YZ is the shortest side of ?XYZ.

MA.912.G.4.7 Apply the inequality theorems
triangle inequality, inequality in one triangle,
and the Hinge Theorem.
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Geometry Mini-Lesson
Which of the following lists the angles from
least to greatest in measurement?

1. X, Y, Z
2. Z, Y, X
3. Y, X, Z
4. X, Z, Y

MA.912.G.4.7 Apply the inequality theorems
triangle inequality, inequality in one triangle,
and the Hinge Theorem.
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Geometry Mini-Lesson
Thierry is monitoring two jets passing by his
airport on radar as shown in the figure below. If
A 30 at noon, and A 15 at 1230, what can
Thierry conclude about the distance between the
two flights?

1. The distance between Flight 815 and Flight 630 is
   less at 1230 than at noon.
2. The distance between Flight 815 and Flight 630 is
   greater at 1230 than at noon.
3. The distance between Flight 815 and Flight 630 is
   the same at 1230 as it was at noon.
4. The distance between Flight 815 and Flight 630
   has not changed significantly between 1230 and
   noon.

MA.912.G.4.7 Apply the inequality theorems
triangle inequality, inequality in one triangle,
and the Hinge Theorem.
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Geometry Mini-Lesson
Given the figure, which of the following answer
choices could be the length of AB ?

1. 7
2. 10
3. 13
4. 20

MA.912.G.4.7 Apply the inequality theorems
triangle inequality, inequality in one triangle,
and the Hinge Theorem.
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Geometry Mini-Lesson
Given the figure at left, which of the following
answer choices is true?

1. WX gt ZY
2. WZ gt XZ
3. XY gt WX
4. XZ gt ZY

MA.912.G.4.7 Apply the inequality theorems
triangle inequality, inequality in one triangle,
and the Hinge Theorem.