Question

7. Given: AB CD, BD =DE
Prove: AD = CE

Statements
Reasons
1.AB = CD, BD = DE
1.given
2.
2. Definition of Congruence
3. AB + BD - AD
3.
4. CD + DEAD
4.
5.
5. Segment Addition Postulate
6. AD CE
6.
7.
7. Definition of Congruence

Answer 1

Answer:

Step-by-step explanation:

Given that Given: AB = CD, BD =DE

The following addition postulates are true;

AB+BD = AD......  1

CD+DE = CE...... 2

Substituting AB = CD, BD =DEinto equation 1, the equations will become;

CD+DE = AD......  3

Subtract equation 2 from 3;

CD -CD+DE-DE = CE - AD

0+0 = CE-AD

0 = CE-AD

CE-AD = 0

Add AD to both sides

CE-AD+AD = 0+AD

CE = AD

AD = CE (Proved)

Answer 2

Answer:

1: correct, given

2: AB≅DE

3: Segment addition postulate

4: Segment addition postulate

5: CD+DE=CE

6: Symmetric

7: BD≅CD

Step-by-step explanation:

Reflexive Property of Congruence

AB is congruent to AB

Symmetric Property of Congruence

If AB is congruent to CD, then CD is congruent to AB

Transitive Property of Congruence

If AB ≅ CD and CD ≅ EF, then AB ≅ EF.

Definition of Congruence

Two segments or angles that are congruent have the same measures

Definition of midpoint

A point that divides a segment into two congruent segments

Segment Addition Postulate

If B is between A and C, then AB + BC = AC

Definition of bisector

a line or segment that intersects a segment or angle and divides it into two congruent halves

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ALSO: NOT 100% sure on these-