Given quadrilateral ABCD,ABllDC, diagonal AC.
we can prove that angle 1= angle 2, but cannot prove angle 3=angle4 Why is this. What must be true about the sides of the Quadrilateral in order to prove that angle 3 is congruent to angle 4?
My answer:
The sides of the quadrilateral must be parellel and that the coresponding angles are congruent to each other. Am I on the right path here? Help pleeeeeeese!
Thanks much
You're on the right path! In order to prove that angle 3 is congruent to angle 4, certain conditions about the sides of the quadrilateral need to be satisfied.
When you mentioned that the sides of the quadrilateral must be parallel, you were correct. Specifically, for angle 3 and angle 4 to be congruent, it is necessary for the quadrilateral ABCD to be a parallelogram.
In a parallelogram, opposite sides are parallel, which implies that opposite angles are congruent. Therefore, if AB || DC, it means that angle 1 = angle 2, as corresponding angles with parallel lines. However, angle 3 and angle 4 are not automatically congruent unless the quadrilateral is a parallelogram.
So, to prove that angle 3 is congruent to angle 4, you need to state that the quadrilateral ABCD is a parallelogram as an additional assumption. Then, based on the properties of parallelograms, you can conclude that angle 3 = angle 4.