Question

a#16: textbook 1-123 to 1-127

1. if no sides of a triangle have the same length, the triangle is called scalene (pronounced scale-een). and, as you might remember, if the triangle has two sides that are the same length, the triangle is called isosceles. use the markings in each diagram below to decide if δabc is isosceles or scalene. assume the diagrams are not drawn to scale. homework help

a. diagram of triangle abc with two sides marked equal
b. diagram of triangle abc with different markings
c. abdc is a square diagram of square abdc with diagonal bc

Explanation:

Part a

Step1: Analyze side markings

In $\triangle ABC$, sides $AC$ and $BC$ have the same tick mark, meaning $AC = BC$.

Step2: Determine triangle type

Since two sides are equal, by the definition of an isosceles triangle (two sides of equal length), $\triangle ABC$ is isosceles.

Part b

Step1: Analyze side markings

In $\triangle ABC$, side $AB$ has two tick marks, side $BC$ has three tick marks, and side $AC$ has one tick mark. So all sides have different numbers of tick marks, meaning all sides are of different lengths.

Step2: Determine triangle type

Since no two sides are equal, by the definition of a scalene triangle (no sides of equal length), $\triangle ABC$ is scalene.

Part c

Step1: Use square properties

In square $ABDC$, all sides are equal, so $AC = AB$ (sides of a square). Also, $BC$ is a diagonal. But in $\triangle ABC$, $AC$ and $AB$ are sides of the square, so $AC = AB$.

Step2: Determine triangle type

Since two sides ($AC$ and $AB$) are equal, by the definition of an isosceles triangle, $\triangle ABC$ is isosceles.

Answer:

a. $\triangle ABC$ is isosceles.
b. $\triangle ABC$ is scalene.
c. $\triangle ABC$ is isosceles.