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**Lesson 5 – 6 Inequalities in Two Triangles**

Geometry Lesson 5 – 6 Inequalities in Two Triangles Objective: Apply the Hinge Theorem or its converse to make comparisons in two triangles. Prove triangle relationships using the Hinge Theorem or its converse.

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**Inequalities in Two Triangles**

Hinge Theorem If two sides of a triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle.

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**Converse of Hinge Theorem**

If two sides of a triangle are congruent to two sides of another triangle, and the third side in the first triangle is longer than the third side in the second triangle, then the include angle measure of the first triangle is greater than the included angle measure in the second.

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**Compare the given measures**

WX and XY WX < XY

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**Compare the given measures**

JK and MQ JK > MQ

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**Compare the given measures**

AD and BD AD > BD

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**Real World Group A is farther from camp since the included angle is**

Two groups of snowmobilers leave from the same base camp. Group A goes 7.5 miles due west and then turns 35 degrees north of west and goes 5 miles. Group B goes 7.5 miles due east then turns 40 degrees north of east and goes 5 miles. At this point, which group is farther from the base camp? Explain. Group A is farther from camp since the included angle is larger than Group B. Draw a picture:

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**Find the range of possible values for x.**

Angle has to be greater than 0, but less than 180. 6x + 15 < 180 6x + 15 > 0 6x + 15 > 65 Don’t have to solve since we already said has to be greater than 65. Double check each time! 6x < 165 6x > 50

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**Find the range of possible values for x.**

Don’t have to solve since we already said has to be less than 141. Double check each time! 9a < 126 9a > -15 a < 14

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**Find the range of possible values for x.**

The length of a side must be positive. Do not need < 180 since 180 is for an angle not a side, and side has no limit on length. 5x + 2 < 47 5x + 2 > 0 5x < 45 5x > -2 x < 9

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Homework Pg – 8 all, 10 – 22 E, 38, 44 – 58 E

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1 Inequalities In Two Triangles. Hinge Theorem: If two sides of 1 triangle are congruent to 2 sides of another triangle, and the included angle of the.

1 Inequalities In Two Triangles. Hinge Theorem: If two sides of 1 triangle are congruent to 2 sides of another triangle, and the included angle of the.

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