6th Grade Math Textbook, Fundamentals

Lesson 9-8 for exercise sets. &KDSWHU 

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Use the figure to answer the questions.

1. How many triangles are in the figure?

2. How many are equilateral triangles?

3. How many are obtuse isosceles triangles?

Can the set of given measurements be used to form a triangle?

Write yesor no. Justify your answers.

4. 2 m, 6 m, 9 m 5. 4.5 ft, 7 ft, 3.2 ft 6. 5 in., 12 in., 13 in.

Write trueor false.

7. Every acute triangle has three acute angles.

8. All scalene triangles are obtuse triangles.

9. All isosceles triangles are right triangles.

10.Discuss and Write Explain why there cannot be a right obtuse triangle.

For triangle XYZ, XY3 cm and YZ4 cm.

What are the possible lengths for ZX?

Use the Triangle Inequality Theorem.

ZX 3  4

ZX 4  3

So the length for ZXis between 1 cm and 7 cm,

or 1 cm ZX7 cm.

1

According to this theorem, if A, B, and Care points in a plane:

CAABBC

CA|ABBC|

You can use the Triangle Inequality Theorem to find the

rangeof numbers that could be the missing length of the

third side of the triangle given the lengths of the other

two sides.

A

B

C

Key Concept

Triangle Inequality Theorem

The third side of a triangle must be:

• less than the sum
  of the other sides; and


• greater than the difference
  of the other sides.

A C

FD

B

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GL

E

The states that the length

of the third side of a triangle is always less than the sum

of the lengths of the other two sides and greater than

their difference.

Triangle Inequality Theorem

a b

c

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