Can someone please help me with these geometry proofs?

Question

Can someone please show these proofs in no more than 4-5 steps. Starting with the Given and ending with the Prove. Use the statement and reason column idea. Thanks! These are a headache. 

1) Given: AB=CD on line AD
    Prove: AC=BD

2) Given: <A is congruent to <C, and line DC is parallel to ray AB
    Prove: line DA is parallel to CB (picture is of plane ABCD)

3) Given: <1 and <2 are vertical, and <1 and <2 are supplementary
    Prove: line KT is perpendicular to line NG (KT is on a line, and NG crosses that line to make it vertical.)

Answer 1

1) you have a website for this problem

 

2) here are some ideas for problem 2 according to your description...

    <A≅<C Given

    draw diagonal DB which is a transversal since AB ll DC

    <BDC≅<ABD  alternate interior angles

    <ADB≅<DBC  alternate interior angles

     m<BDA+m<BDC=m<ADC   angle addition postulate

     do the same for angles ABD and DBC

     also m<BDC=m<ABD congruent angles have equal measures

           m<ADB=m<DBC  same reason as above

          m<BDC+m<ADB=m<ABD+m<DBC   addition property of equality

     do the same for angles ABD and DBC

    m<ADC=m<ABC  <ADC=<ADB+<BDC and <ABC=??

    basically <A=<C Given and <D=<B which was just proved

    quadrilateral ABCD is a parallelogram because both pairs of opposite angles are congruent

    DA ll CB opposite sides of a parallelogram are parallel

 

3) line KT intersects line NG  Given

    <1 and <2 are vertical angles   Given

    <1=<2 in measure   vertical angles have equal measure

    <1 and <2 are supplementary  ??

    <1+<2=180º  definition of ??

    <2+<2=180º substitution

    2*m<2=180º

        m<2=90º division property of equality

        m<1=90º  <1 and <2 have equal measures because they are vertical angles

       line KT is perpendicular to line NG   perpendicular lines intersect to form ???

  

Answer 2

Hi Haley,

 

Mark M has made a couple of good suggestions.

 

Constructing geometry proofs is a skill that does come with practice.

 

Below is a link to a sample proof for your 1st problem to help get you started:

 

https://dl.dropbox.com/s/semyk2ah306y5x8/Sample_Proof_Problem_1.png?raw=1

 

As Mark M advised, tutors will be happy to review your work and help fill in any gaps.

 

God bless, Jordan.