Suppose that you know that a golfer plays the first hole of a golf course with an infinite number of holes and that if this golfer plays one hole, then the golfer goes on to play the next hole. Prove that this golfer plays every hole on the course.

hello,

elba writes the following proof for the theorem: if the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram:

elba's proof

1. for triangles aob and cod, angle 1 is equal to angle 2 as they are vertical angles.

2. ao = oc and bo = od because it is given that diagonals bisect each other.

3. therefore, the triangles aob and cod are congruent by sas postulate.

4. similarly, triangles aod and cob are congruent.

5. by cpctc, angle abd is equal to angle cdb and angle adb is equal to angle cbd.

6. as the are congruent, the opposite sides of quadrilateral abcd are parallel.

7. therefore, abcd is a parallelogram.

which is the missing phrase in elba's proof?

answer - opposite

if a polygon ab c d e is transformed to congruent polygon mn o p q, then following possibilities can happen

1. rotation                 2. reflection             3. translation   4. reflection and then translation or vice versa     5. rotation and then reflection or vice versa     6. translation and rotation   or vice versa   7. all of three , rotation, then reflection and then translation or in any order.  

we will get a congruent polygon m n o p q which is congruent to a b c de.

now , polygon   m n o p q is translated 3 units right and 5 units down to get a   congruent polygon, v w x y z, so if vertices of   polygon   m n o p q is m(x,y), n(u,v), o(p,q), p(r,s) and   q(a,b)   this, then vertices of polygon, v w x y z will be ,v(x+3,y-5), w(u+3,v-5),o(p+3,q-5),p(r+3,s-5),q(a+3,b-5).