SOLUTION: I have two problems that I need help: Problem #1: Prove triangle ABC is congruent to triangle EDC. If, I have been given: line segment AE & BD are line segments intersecting

Question 28921: I have two problems that I need help: Problem #1:
Prove triangle ABC is congruent to triangle EDC. If, I have been given: line segment AE & BD are line segments intersecting at point C. And line segment AC is congruent to line segment EC. And line segment BC is congruent to line segment DC.
I wrote my STATEMENTS and REASONS as follows:
STATEMENT: 1. Line segments AE & DB intersect at C.
REASON: 1. Given.
STATEMENT: 2. Line segments AC & EC are congruent.
REASON: 2. Given.
STATEMENT: 3. Line segments BC & DC are congruent.
REASON: 3. Given.
STATEMENT: 4. Angles ACB & ECD are congruent.
REASON: 4. Vertical angles are congruent (Theorem)
STATEMENT: 5. Triangles ABC & EDC are congruent.
REASON: 5. (SSS are congruent to SSS). If three sides of one triangle are congruent, respectively, to three sides of a second triangle, then the triangles are congruent. (Postualte)
I'm not sure if Step 4 is correct or if I can even write that statement.
Please help.
Problem #2:
Prove triangle ADB is congruent to triangle ACE. If, I have been given: line segment AD is congruent to line segment AC. And line segment AB is congruent to line segment AE.
I wrote my STATEMENTS & REASONS as follows; does it make sense? if not, how do I approach this problem?:
STATEMENT: 1. Line segments AD & AC are congruent.
REASON: 1. Given.
STATEMENT: 2. The measurement of line segment AD is equal to the measurement of line segment AC.
REASON: 2. Two line segments are congruent if, and only if, they have the same measure. by Definition.
STATEMENT: 3. Line segments AB & AE are congruent.
REASON: 3. Given.
Now, I'm not sure where to go from here? Do I try to solve it by making all the sides congruent to each other?
Please help.
Sincerely, "nani"

Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
GOOD JOB!KEEP IT UP!YOU HAVE GOT IT ALMOST CORRECT
SEE BELOW
I have two problems that I need help: Problem #1:
Prove triangle ABC is congruent to triangle EDC. If, I have been given: line segment AE & BD are line segments intersecting at point C. And line segment AC is congruent to line segment EC. And line segment BC is congruent to line segment DC.
I wrote my STATEMENTS and REASONS as follows:
STATEMENT: 1. Line segments AE & DB intersect at C.
REASON: 1. Given.
STATEMENT: 2. Line segments AC & EC are congruent.
REASON: 2. Given.
STATEMENT: 3. Line segments BC & DC are congruent.
REASON: 3. Given.
STATEMENT: 4. Angles ACB & ECD are congruent.
REASON: 4. Vertical angles are congruent (Theorem) VERTICALLY OPPOSITE ANGLES ARE EQUAL..THAT IS THE CORRECT STATEMENT.
STATEMENT: 5. Triangles ABC & EDC are congruent.
REASON: 5. (SSS are congruent to SSS). If three sides of one triangle are congruent, respectively, to three sides of a second triangle, then the triangles are congruent. (Postualte) ...NO THEOREM IS SAS..2 SIDES AND INCLUDED REPEAT INCLUDED ANGLES ARE EQUAL RESPECTIVELY THE CORRESPONDING SIDES AND INCLUDED ANGLE , THEN THE 2 TRIANGLES ARE CONGRUENT.
I'm not sure if Step 4 is correct or if I can even write that statement.IT IS OK BUT FOR THE SLIGHT MODIFICATION SUGGESTED.
REASON 5 IS TO BE CHANGED AS GIVEN .
Please help.
Problem #2:
Prove triangle ADB is congruent to triangle ACE.
IS IT THE SAME FIGURE AS ABOVE?THEN ACE IS A STRAIGHT LINE.IT IS NOT A TRIANGLE.
IF NOT GIVE THE FIGURE OR ITS DESCRIPTION TO COMMENT..
If, I have been given: line segment AD is congruent to line segment AC. And line segment AB is congruent to line segment AE.
UNLESS YOU CORRECT THE ABOVE THSE DO NOT GIVE ANY IDEA OR MEANING
I wrote my STATEMENTS & REASONS as follows; does it make sense? if not, how do I approach this problem?:
STATEMENT: 1. Line segments AD & AC are congruent.
REASON: 1. Given.
STATEMENT: 2. The measurement of line segment AD is equal to the measurement of line segment AC.
REASON: 2. Two line segments are congruent if, and only if, they have the same measure. by Definition.
STATEMENT: 3. Line segments AB & AE are congruent.
REASON: 3. Given.
Now, I'm not sure where to go from here? Do I try to solve it by making all the sides congruent to each other?
Please help.
Sincerely, "nani"

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