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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

6. Inequalities in One Triangle

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Exercise 17 Page 329

Start by finding the third angle of the triangle using the Triangle Angle-Sum Theorem.

TU, UV, TV

Practice makes perfect

We want to order the sides of the given triangle from shortest to longest.

First, let's find the third angle of the triangle using the Triangle Angle-Sum Theorem.

m∠ T + m∠ U+m∠ V=180

m∠ U= 90, m∠ V= 30

m∠ T + 90+ 30=180

▼

Solve for m∠ T

Add terms

m∠ T+120=180

LHS-120=RHS-120

m∠ T=60

Let's add this newly found measurement to the triangle.

We know that, if two angles of a triangle are not congruent, then the longer side lies opposite the larger angle. Applying this fact, we can order the sides from shortest to longest. ccccc 30^(∘) & < & 60^(∘) & < & 90^(∘) m∠ V & < & m∠ T & < & m∠ U TU & < & UV & < & TV

Subchapter links

Lesson Check p.328

Practice and Problem-Solving Exercises p.328-331

Standardized Test Prep p.331

Mixed Review p.331