Question

Proof for parallelogram

Answer 1

given PQRS is a parallelogram
prove PR and QS bisect each other at T

Answer 2

PR is not bisected if the two parts are 1 and 3

Answer 3

by definiton of paralleogram, PQ=SR, and PQ II SR

Answer 4

by alternate interior angles, <1=<3 and <2=<4
by ASA, triangles STR=QTP.
then u should be able to fill up the rest using CPCTC and definition of bisector

Answer 5

We need to prove triangle PTQ is congruent to triangle STR.
By parallelogram definition, lines PQ = SR
Since PQ is parallel to SR then
Angle QPT = angle TRS and angle PQT = angle TSR
using ASA triangle PTQ is congruent to triangle STR and therefore
line TS = TQ and line PT = line PR

Answer 6

so if we put this into a 2 column proof it would be

Answer 7

PQRS is a parallelogram
reason= PQ=SR
PQ is parallel to SR
reason=Angle QPT = angle TRS and angle PQT = angle TSR
Angle are congruent
reason=ASA triangle PTQ is congruent to triangle STR
line TS = TQ and line PT = line PR

Answer 8

No.
1. PQRS is paralleogram
R- given
2. PQ=SR and PQ II SR
R- def of paralleogram
3.<1=<3 and <2=<4
R- alternate interior angle theorem
4. Triangle STR=QTP
R-ASA
5. ST=TQ and TP=TR
R-CPCTC
6. SQ bisects PR
R-definition of bisector