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Objectives - PowerPoint PPT Presentation

Objectives. State the inequalities that relate angles and lengths of sides in a triangle State the possible lengths of three sides of a triangle. Angle-Side Relationships in a Triangle. If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side.

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Presentation Transcript

• State the inequalities that relate angles and lengths of sides in a triangle

• State the possible lengths of three sides of a triangle

If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side.

If XZ > XY, then m∠Y > m∠Z.

If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle.

If m∠A > m∠B, thenBC > AC

List the angles from least to greatest in measure.

Since the sides can be ordered by 1.8cm, 2.7cm, and 3.9cm, the angles opposite to those sides respectively are ∠V, ∠M, and ∠O.

Triangle Inequality Theorem:

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

XY + YZ > XZ

YZ + ZX > YX

ZX + XY > ZY

Is it possible to have a triangle with side lengths of 15, 12, 9 ?

The sum of any two sides must be greater than the remaining side.

15 + 12 > 9 Yes

12 + 9 > 15 Yes

15 + 9 > 12 Yes

So the three lengths satisfy the Triangle Inequality Theorem and are possible in a triangle.

Given that two sides of a triangle measure 9 and 15, what are the possible values of the third side’s lengths?

Lower limit = 15 – 9 = 6 (x + 9 > 15)

Upper limit = 15 + 9 = 24 (15 + 9 > x)

6 < x < 24