Understanding Triangle Inequalities and the Hinge Theorem in Geometry
This guide explores the concept of triangle inequalities and the Hinge Theorem, crucial for determining the lengths of triangle sides. We will cover the conditions for forming a triangle, including the triangle inequality theorem that states the sum of the lengths of any two sides must exceed the length of the third side. Additionally, the Hinge Theorem and its converse are discussed to analyze relationships among triangle sides and angles. Practice questions and answers enhance understanding of these fundamental concepts in geometry.
Understanding Triangle Inequalities and the Hinge Theorem in Geometry
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Presentation Transcript
Jeopardy Triangle Inequality Triangle Sides Hinge Theorem Converse of Hinge Theorem Q $100 Q $100 Q $100 Q $100 Q $200 Q $200 Q $200 Q $200 Q $300 Q $300 Q $300 Q $300 Q $400 Q $400 Q $400 Q $400 Q $500 Q $500 Q $500 Q $500 Final Jeopardy
$100 Question from Triangle Sides The following subset an appropriate set of triangle lengths? (True/False) [ 25, 25, 25]
$200 Question from Triangle Sides The following subset an appropriate set of triangle lengths? (True/False) [ 3, 6, 3]
$300 Question from Triangle Sides The following subset an appropriate set of triangle lengths? (True/False) [ 1, 2, 3]
$400 Question from Triangle Sides The following subset an appropriate set of triangle lengths? (True/False) [ 4, 6, 3]
$500 Question from Triangle Sides 1013, 2238, 1224,
$100 Question from Triangle Inequality Find an interval of lengths for the third Side of a triangle with side lengths 4 and 8.
$100 Answer from Triangle Inequality 4< x < 12
$200 Question from Triangle Inequality Find an interval of lengths For the third side of a triangle With side lengths 17 and 34.
$200 Answer from Triangle Inequality 17 < x < 51
$300 Question from Triangle Inequality Find an interval of the last side Of a triangle that has side lengths 9.2 And 3.4
$300 Answer from Triangle Inequality 5.8 < x < 12. 6
$400 Question from Triangle Inequality Find the interval of lengths for the last Side of a triangle with lengths 1031 and 735.
$400 Answer from Triangle Inequality 296 < x < 1766
$500 Question from Triangle Inequality Find the interval of lengths for The last side of a triangle with side Lengths “a” and “b”, given that a > b
$500 Answer from Triangle Inequality a-b < x < a + b
$500 Question from Hinge Theorem Triangle 1 has side lengths 4 and 3, And the included angle measure is 91. Triangle 2 has side lengths 4 and 3, And the included angle measure is 109. Which triangle has the longer third side?
$500 Answer from Hinge Theorem Triangle 2
$500 Question from Hinge Theorem Converse In order for the Converse of the Hinge Theorem to be true, ______ sides need to be congruent in two different triangles.
$500 Answer from Hinge Theorem Converse Two or three
$100 Question from Hinge Theorem Converse Your Text Here
$100 Answer from H5 Your Text Here
$200 Question from H5 Your Text Here
$200 Answer from H5 Your Text Here
$300 Question from H5 Your Text Here
$300 Answer from H5 Your Text Here
$400 Question from H5 Your Text Here
$400 Answer from H5 Your Text Here
$500 Question from H5 Your Text Here
