NEED HELP! QUICK PLEASE.

G

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Hi everybody! Its me again. I have some problems again! Well I think I have the fisrt one rigth but the second and the third one its a different story. I don't know why but I don't get these last two problems. I think the first one its right but I would like to see if you can check it anyways, please. THANKS IN ADVANCE.

Code: 
 1ST ONE
Given: Triangle HPK & Traingle HMK are isosceles with base HK.
Prove:Triangle HPM is congruent to Triangle KPM

 H            J             K
  _________________
   \ *   1       l       2  */
    \     *      l     *    /
      \           * P     /   
        \         l       /     
          \       l     /
            \     l    /
              \   l   /
                \ l /
                  *
                  M

THIS IS WHAT I GOT FOR THE FIST ONE!
 STatements                              REasons
1.Triangle HPK & T. HMK are   1. GIVEN
isosceles w/ base HK
2.KM is congruent to HM &       2.DEFINITION OF ISOSCELES TRIANGLE 
KP is congruent to HP
3.PM is congruent to PM &        3. REFLEXIVE PROPERTY
JP is congruent to JP
4. Triangle HPM is congruent      4. S.S.S.
to Triangle KPM

THIS IS THE SECOND ONE! I COULDN'T DO IT, BECAUSE I DIDN'T KNOW WHAT TO USE IN THE REASONS AND EITHER IN THE STATEMENTS. PLEASE HELP ME GETTING IT DONE. PLEASE.

Code: 
                       P
                       *
                    /  *  \
                 /   *  *   \
               /    *    *    \
             /     *      *     \
           /      *        *      \ 
         /     1 * 3     4* 2    \
        ++++*+++++*++++
       A         B          C        D
   
    GIVEN: Triangle ADP, <3 congruent to <4, AB congruent to DC, PB congruent to PC.
    PROVE: Triangle ABP congruent to Triangle DCP

STATEMENTS                                                  REASONS 
1. Triangle ADP, <3 congruent to <4,                1. GIVEN 
AB congruent to DC, PB congruent to PC.

PLEASE HELP ME WITH THE FOLLOWING STATEMENTS & REASONS, please!
THIS IS THE THIRD ONE & AS THE SAME AS TWO I DIDN'T KNOW HOW TO DO IT! PLEASE HELP. THANKS AGAIN!

Code: 
 Third one     E 
                    *
                   /    *
                 /           *         J
            F  /___________*___________G
                                        *                     /
                                             *               /
                                                 *         /
                                                      * /
                                                        H

GIVEN: FE is Perpendicular EH, HG is Per. to EH, J is the midpoint of EH
PROVE: Triangle FEJ congruent to Triangle GHJ

Statements                                        Reasons 
1.FE is Perpendicular EH, HG is            1. GIVEN
Per. to EH, J is the midpoint of EH


PLEASE HELP ME THESE ARE THREE OF THE PROBLEMS I'M HAVING TROUBLE WITH. THE OTHER FIVE I GOT THEM RIGTH. I JUST NEED HELP IN THESE 3 PLEASE. THANKS AGAIN!
 
Code: 
                       P 
                       * 
                    /  *  \ 
                 /   *  *   \ 
               /    *    *    \ 
             /     *      *     \ 
           /      *        *      \ 
         /     1 * 3       4* 2    \ 
        ++++*+++++*++++ ++++++++
       A         B          C        D 
    
    GIVEN: Triangle ADP, <3 congruent to <4, AB congruent to DC, PB congruent to PC. 
    PROVE: Triangle ABP congruent to Triangle DCP 

STATEMENTS                                                  REASONS 
1. Triangle ADP, <3 congruent to <4,                1. GIVEN 
AB congruent to DC, PB congruent to PC.


Hi, Bismarck,

You’re first problem looks fine. On the second problem, I’ll give you some hints. You can show triangle congruency by S.A.S. However, to do that, you must show <1 is congruent to <2. Since triangle BPC is isosceles, and angles 3 and 4 are congruent, that shouldn’t be too hard. Note that angles 1 and 3 are a linear pair, which means they are supplementary. The same goes for angles 4 and 2. Therefore, <1 = (180 - <3) = (180 - <4) = <2, either by invoking the transitive property or the substitution property of equality.

Hope that helps.
 
Code: 
 Third one     E 
                    * 
                   /    * 
                 /           *         J 
            F  /_______________________*_______________________G 
                                        *                     / 
                                             *               / 
                                                 *         / 
                                                      * / 
                                                        H 

GIVEN: FE is Perpendicular EH, HG is Per. to EH, J is the midpoint of EH 
PROVE: Triangle FEJ congruent to Triangle GHJ 

Statements                                        Reasons 
1.FE is Perpendicular EH, HG is            1. GIVEN 
Per. to EH, J is the midpoint of EH


You can show triangle congruency using A.S.A. <EJF is congruent to <HJG by vertical angles. Segment EJ is congruent to segment HG by definition of bisect. Finally, <FEJ is congruent to <GHJ by definition of perpendicularity.
 
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