Some things in this topic i struggle with are proving a perpendicular bisector of a line segment, to prove that a line is bisected, and proving that a hexagon consists of equilateral triangles.
1) Imagine if there was a line segment, and they asked you to bisect it using a compass,,, how would you prove that the line is bisected?
Would you use the properties of a rhombus to do your proof? how would you approach this...
2) Imagine a line segment, and being asked to construct the perpendicular bisector for it,,,then being asked to prove that the line that you just drew is the perpendicular bisector for the line segment...
3) Imagine a hexagon,,,it could be inscribed in a circle or just a normal hexagon,,,,pretend you constructed it by inscribing it inside a circle...and then being asked prove that the hexagon you just drew consists of equilateral triangles....
I really struggle with proofs especially for the topics listed above and parallelograms...
if somebody could explain these to me I would really appreciate it.
Not sure our class has just touched the surface of constructions. we just started constructing congruent triangles lol very basic
1. I think you can prove the segment is bisected by showing that it is divided into TWO EQUAL lengths, so probably you have to use your compass and make two swoops that are equal in swoop-length, I don't know.
If a segment is divided into two congruent parts, then it is bisected.
2. I think you just have to show that they form 90 degrees, and that like number 1, it divides the segment into TWO EQUAL parts.
Since all radii of a circle are congruent, you probably have to show that the triangles of the hexagon meet at the center.
If you do this, you proved two of their corrresponding sides are congruent. Then using vertical angles, you can prove all of the included angles of their sides are congruent.
So by doing this, you can use SAS to show that ALL of the triangles are congruent.
Then you have to show that ONE of the triangles is equilateral, which makes ALL of the other triangles equilateral as you just proved them all to be congruent
A triangle is equiliateral if and only if all of its corresponding sides are equal OR if all of its corresponding angles are equal.
Sorry, what I said is quite confusing, proofs are hard.
I haven't learned construction proving quite yet, so don't take my answer seriously.