Look at the quadrilateral shown below:

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

mellissa’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. the are congruent by sas postulate

4. similarity, triangles aod and cob and congruent

5. by cpctc, ab is equal to dc

6. by cpctc, ad is equal to bc

7. as the opposite sides are congruent, the quadrilateral abcd is a parallelogram.

which is the missing phrase in melissa’s proof?

a. angles adb and cbd
b. angles aob and cod
c. triangles adb and cbd
d. triangles aob and cod

i dont have an answer

step-by-step explanation:

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.