Question

11 multiple choice 1 point name the side opposite ∠wxy. 12 multiple choice 1 point which set of numbers could represent the lengths of the sides of an isosceles triangle?

Explanation:

Question 11

Step1: Recall the definition of opposite side

In a triangle, the side opposite an angle is the side that does not form the angle.
For \(\angle WXY\), the sides forming the angle are \(\overline{WX}\) and \(\overline{XY}\).

Step2: Identify the opposite side

So the side opposite \(\angle WXY\) is \(\overline{WY}\)

Step1: Recall the triangle inequality theorem

For a set of numbers \(a,b,c\) to be the side lengths of a triangle, \(a + b>c\), \(a + c>b\) and \(b + c>a\). For an isosceles triangle, at least two sides are equal.

Step2: Check each option

• Option \(\{3,45,5\}\): \(3 + 5=8<45\), does not satisfy the triangle - inequality theorem.
• Option \(\{6,6,5\}\): \(6+6 = 12>5\), \(6 + 5=11>6\), satisfies the triangle - inequality theorem and has two equal sides.
• Option \(\{5,5,10\}\): \(5+5=10\), does not satisfy the triangle - inequality theorem (\(a + b>c\) with \(a = 5\), \(b = 5\), \(c = 10\)).
• Option \(\{1,1,3\}\): \(1+1=2<3\), does not satisfy the triangle - inequality theorem.

Answer:

\(\overline{WY}\)

Question 12