Question

Triangle DEF has sides DE = 12, EF = 6, and DF = 8. Is triangle DEF congruent to triangle ABC? Show your work using the distance formula.

Answer 1

not congruent

Explanation:

Triangle is a polygon shape with three sides and three angles. There are different types of triangles such as obtuse triangle, scalene triangle, equilateral triangle an isosceles triangle.

Two triangles are said two be congruent if all the the three sides as well as the three angles are equal.

Triangle DEF and triangle ABC would be congruent if their sides are equal. Given that for triangle DEF, DE = 12, EF = 6, and DF = 8 while for triangle ABC in the image attached we can see that one side = 6, the other side= 8. The length of the third side is gotten using distance formula:

`Distance=√((x_2-x_1)^2+(y_2-y_1)^2)\\\\Distance=√((12-4)^2+(14-8)^2) =10`

Since the last side = 10 which is not equal to 12, hence triangle DEF is not congruent to triangle ABC