Question

1. classify each triangle by its angles and sides. a. △abe. b. △bec. c. △def. d. △cde. 2. given the coordinates, classify △qrt by its sides. q(-2, -1), r(1, 5), t(-8, -4)

Explanation:

Step1: Recall distance - formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Calculate length of $QR$

For points $Q(-2,-1)$ and $R(1,5)$, we have $x_1=-2,y_1 = - 1,x_2=1,y_2 = 5$.
$QR=\sqrt{(1+2)^2+(5 + 1)^2}=\sqrt{9 + 36}=\sqrt{45}=3\sqrt{5}$.

Step3: Calculate length of $RT$

For points $R(1,5)$ and $T(-8,-4)$, we have $x_1=1,y_1 = 5,x_2=-8,y_2=-4$.
$RT=\sqrt{(-8 - 1)^2+(-4 - 5)^2}=\sqrt{81+81}=\sqrt{162}=9\sqrt{2}$.

Step4: Calculate length of $QT$

For points $Q(-2,-1)$ and $T(-8,-4)$, we have $x_1=-2,y_1=-1,x_2=-8,y_2=-4$.
$QT=\sqrt{(-8 + 2)^2+(-4 + 1)^2}=\sqrt{36 + 9}=\sqrt{45}=3\sqrt{5}$.

Step5: Classify the triangle

Since $QR = QT=3\sqrt{5}$ and $RT = 9\sqrt{2}$, $\triangle QRT$ is an isosceles triangle.

Answer:

$\triangle QRT$ is an isosceles triangle.