Question

unit 1: convincing arguments
unit review
content objective: swbat review and apply properties of triangles and quadrilaterals, and proof writing
procedural objective: swbat use information about angles and sides in a triangle to answer questions.
language objective: swbat read and answer, in writing, unit review questions with the assistance of notes.
launch:
attempted on time: mpppp
here is triangle xyz.
a. list one possible side length for xz: 4.1
b. list one impossible side length for xz: 10

Explanation:

Step1: Apply triangle - inequality theorem

The triangle - inequality theorem states that for any triangle with side lengths \(a\), \(b\), and \(c\), the following three inequalities must hold: \(a + b>c\), \(a + c>b\), and \(b + c>a\). In \(\triangle XYZ\) with \(XY = 10\) and \(YZ = 5\), let \(a = 10\), \(b = 5\), and \(c\) be the length of \(XZ\). Then \(10+5>c\) (i.e., \(c < 15\)) and \(10 + c>5\) (always true for non - negative \(c\)) and \(5 + c>10\) (i.e., \(c>5\)). So \(5 < c<15\).

Step2: Find a possible side - length

Since \(5 < c<15\), a possible value for the length of \(XZ\) could be \(9\) (any value in the range \(5 < c<15\) would work).

Step3: Find an impossible side - length

An impossible value for the length of \(XZ\) could be \(10\) (because the question seems to imply non - congruent side lengths in the context of just giving one example, and also values outside the range \(5 < c<15\) like \(15\) or \(20\) or \(1\) would be impossible. Here we take \(10\) as per the given answer in the image for illustration, but other values outside the range are also valid non - examples).

Answer:

a. 9
b. 10