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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

3. Inequalities in One Triangle

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Exercise 16 Page 430

Consider Theorem 5.10 about Angle-Side Relationships in Triangles.

Angles: ∠ H, ∠ J, ∠ K
Sides: JK, KH, HJ

Practice makes perfect

On the diagram, we are given the measures of all the angles in △ HJK.

We can see that ∠ H is the smallest angle, followed by ∠ J and then ∠ K.

m ∠ H < m ∠ J < m ∠ K ⇕ 57 ^(∘) < 61 ^(∘) < 72 ^(∘) Next, let's consider Theorem 5.10 about Angle-Side Relationships in Triangles.

Angle-Side Relationships in Triangles
If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle.

Now, considering this theorem, we will look for the corresponding opposite sides. cc Angle & Opposite Side [0.5em] ∠ H & JK [0.5em] ∠ J & KH [0.5em] ∠ K & HJ Therefore, we can list the sides in order from smallest to largest. JK < KH < HJ

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Exercises p.430-433