Question

1. triangle abc is an acute isosceles triangle. determine the measure of each of the congruent sides. (round your answer to the nearest tenth.)

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: Assume coordinates

Let's assume the coordinates of the vertices of the triangle from the graph. Suppose $A=(x_1,y_1)$, $B=(x_2,y_2)$ and $C=(x_3,y_3)$.

Step3: Calculate side - length AB

$AB=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step4: Calculate side - length BC

$BC=\sqrt{(x_3 - x_2)^2+(y_3 - y_2)^2}$.

Step5: Calculate side - length AC

$AC=\sqrt{(x_3 - x_1)^2+(y_3 - y_1)^2}$.

Step6: Round to nearest tenth

Round the values of $AB$, $BC$ and $AC$ to the nearest tenth.

Since the coordinates of the vertices are not given in the problem statement, we cannot perform the actual numerical calculations. But the general steps to find the lengths of the sides of the triangle using the distance formula are as above.

Answer:

Without the specific coordinates of the vertices of triangle $ABC$, we cannot give the numerical lengths of the congruent sides. If the coordinates were $(x_1,y_1)$, $(x_2,y_2)$ and $(x_3,y_3)$, we would calculate the distances as $AB=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, $BC=\sqrt{(x_3 - x_2)^2+(y_3 - y_2)^2}$, $AC=\sqrt{(x_3 - x_1)^2+(y_3 - y_1)^2}$ and round to the nearest tenth.