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McGraw Hill Glencoe Geometry, 2012 View details

3. Inequalities in One Triangle

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Exercise 16 Page 348

Consider Theorem $5.10$ about Angle-Side Relationships in Triangles.

Angles: $∠ H,$ $∠ J,$ $∠ K$
Sides: $\overline{J K},$ $\overline{K H},$ $\overline{H J}$

Practice makes perfect

On the diagram, we are given the measures of all the angles in $△ H J K .$

We can see that

∠ H

is the smallest angle, followed by

∠ J

and then

∠ K .

m ∠ H < m ∠ J < m ∠ K ⇕ 5 7^{\circ} < 6 1^{\circ} < 7 2^{\circ}

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.

\underline{g Angle g} ∠ H ∠ J ∠ K \underline{. Opposite Side .} \overline{J K} \overline{K H} \overline{H J}

Therefore, we can list the sides in order from smallest to largest.

J K < K H < H J

Subchapter links

Check Your Understanding p.348

Practice and Problem Solving p.348-350

H.O.T. Problems p.350

Standardized Test Practice p.351

Spiral Review p.351

Skills Review p.351

Exercise 16 Page 348

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