Question

Which conjecture is possible to prove is congruent? A. All quadrilaterals with 4 equal angles B. All triangles with 3 equal angles C. All quadrilaterals with 4 equal sides D. All triangles with 3 equal sides

Answer 1

Answer:  D. All triangles with 3 equal sides

Step-by-step explanation:

Remember, congruence means that the sides are equal and also the corresponding angles:

A) Quadrilaterals with 4 equal angles.

Here we can have, for example, a lot of different rectangles and squares, because all of them have only 45° angles, but a square is not congruent with a rectangle, so this option is not correct.

B) Triangles with 3 equal angles.

Think in the triangles, the 3 angles are 60°,

But we can craft this angle with a lot of different side lengths, so this is not the correct option, so not all the triangles with equal angles are congruent, then this option is incorrect.

C) Quadrilaterals with 4 equal sides: Here we can have a square, or a rhombus, or a parallelogram, so this option is also incorrect.

D) Triangles with 3 equal sides:

Now, we have the set of all the triangles where the length of the 3 sides is the same.

Now, if you have 3 knowed lenghts (the ones shared by the set of triangles) you can only create one triangle with them, this is known as the SSS criterion of congruence for triangles. This is the correct option.