Question

question 7 (im)
which side in the triangle abc is the shortest?
a. segment ab
b. segment ac
c. segment bc
d. impossible to determine
question 8 (im)
lines x and y are parallel.
write an equation that represents the relationship between b and e. explain how you know this equation is always true.

Explanation:

Question 7

Step1: Find the third - angle

The sum of angles in a triangle is 180°. Let the third angle be $\angle A$. So, $\angle A=180^{\circ}-(70^{\circ} + 60^{\circ})=50^{\circ}$.

Step2: Recall angle - side relationship

In a triangle, the shortest side is opposite the smallest angle. The smallest angle is $\angle A = 50^{\circ}$, and the side opposite $\angle A$ is $BC$.

Step1: Identify angle relationship between b and e

Since lines $x$ and $y$ are parallel, $\angle b$ and $\angle e$ are corresponding angles. Corresponding angles formed by parallel lines and a transversal are equal. So the equation is $b = e$.

Step2: Identify angle relationship between b and d

$\angle b$ and $\angle d$ are vertical angles. Vertical angles are equal, so the equation is $b = d$.

Step3: Identify angle relationship between d and e

Since $b = e$ and $b = d$, we can substitute to get $d = e$.

Answer:

C. Segment BC

Question 8