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McGraw Hill Integrated II, 2012 View details

6. Inequalities in Two Triangles

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Exercise 32 Page 460

Use the Converse of the Hinge Theorem.

m∠ FBG

Practice makes perfect

Let's highlight the angles we are asked to compare.

We will focus on triangles △ BFA and △ FBG, and summarize what we know about the sides of these triangles.

Claim	Justification
FA≅BG	Both segments have measure 10.
FG< BA	8<11

Since FB is a common side, triangles △ BFA and △ FBG have two pairs of congruent sides. This means that we can apply the Converse of the Hinge Theorem. FG< BA ⇓ m∠ FBG < m∠ BFA