Prove that the opposite angles of a parallelogram are congruent.

Question

anonymous · Answer

attachment

anonymous · Answer

Someone please help!

mathstudent55 · Answer

You need a two-column proof. The idea here is to use triangles. You prove the triangles are congruent and then the corresponding parts, the opposite angles of the parallelogram are congruent.

anonymous · Answer

Whats the given tho i always get confused on that part

mathstudent55 · Answer

Given: Parallelogram ABCD
Prove: <1 is congruent to <3
          <2 is congruent to <4

mathstudent55 · Answer

St1: Parallelogram ABCD            R1: Given

mathstudent55 · Answer

St2. Segment BC is congr to seg AD    R2: Opp sides of parallelogram are congruent

mathstudent55 · Answer

St3 Seg CD is congr to seg AB.   R3 Opp sides of parallelogram are congr

mathstudent55 · Answer

St 4. Seg BD is congr to seg BD        R4  A seg is congruent to itself

mathstudent55 · Answer

st5. triangle BCD is congr to triangle DAB    R5 SSS
st6 <1 is congr to <3                                  R6 CPCTC

mathstudent55 · Answer

Now pick two other triangles that are congruent that have angles 2 and 4, prove them congruent and then by CPCTC you get <2 congr to <4

anonymous · Answer

okay ill try if i need help I'lll let you know

anonymous · Answer

So would it basically be like <1 and <3 when i try to prove <2 and <4

anonymous · Answer

@mathstudent55

mathstudent55 · Answer

yes