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17 December, 07:08

Consider the triangles shown. If mUTV < mUTS < mSTR, which statement is true?

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Answers (1)
  1. 17 December, 09:31
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    The true statement is UV < US < SR ⇒ 1st statement

    Step-by-step explanation:

    "I have added screenshot of the complete question as well as the

    diagram"

    * Lets revise the hinge theorem

    - If two sides of one triangle are congruent to two sides of another

    triangle, and the measure of the included angle between these two

    sides of the first triangle is greater than the measure of the included

    angle of the second triangle then the length of the third side of the

    first triangle is longer than the length of the third side of the second

    triangle

    * Lets solve the problem

    - The figure has three triangles have a common vertex T

    - m∠UTV < m∠UTS < m∠STR

    - From the hinge theorem above

    ∵ The side opposite to ∠UTV is VU

    ∵ The side opposite to ∠UTS is US

    ∵ The side opposite to ∠STR is SR

    ∵ m∠UTV < m∠UTS < m∠STR

    ∴ UV < US < SR

    * The true statement is UV < US < SR
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