Question

A triangular peak on a backyard shed is trimmed with 3 pieces of 4 ft. molding. The next door neighbor decides to use 12 ft. of molding to add a decorative triangle to his shed. Are the two triangles congruent? Justify your answer.

Answer 1

They can be, if they are equilateral 4-4-4 triangles.
But they can be incongruent, if they are 5-5-2 isosceles triangles or 5.5-5.5-1.

Answer 2

Answer:

D.

Step-by-step explanation:

The options for this question are:

A) yes; Both owners are using 12 linear feet of molding.

B) yes; Since both triangles have 3 sides, they are similar and congruent.

C) yes; Twelve feet divided by 3 sides always gives 4 feet for each side length.

D) not necessarily; The sides of the neighbor's triangles could have different side lengths such as 3, 4, and 5.

The right answer is option D, because not necessarily they are congruent triangles, because they only have have the same perimeter, a equivalent perimeter doesn't imply the same sides or same angles. So, sides of both triangles can have different lengths and they still would be equal in perimeter.

So, they don't necessarily have to be congruent.

Remember that congruence between triangles is demonstrate by finding equivalents corresponding elements, like Side-Side-Side, or Side-Angle-Side, which is not specified in this problem.

Therefore, the right choice is

D) not necessarily; The sides of the neighbor's triangles could have different side lengths such as 3, 4, and 5.