Question

Desmos Introduction to Geometry Proofs
Proof #5 Challenge

Answer 1

Answer:

For statement 2, reason is Segment addition postulate.

Statement 3 and reason is

BD=AC+CD using substitution property of equality.

Statement 4 and reason is

AC+CD=BD using symmetric property of equality

Statement 5 is

BD= BC+CD

Statement 6 and reason is

AC+CD=BC+CD using transitive property of equality

Reason for 7 is

Subtraction property of equality.

Step-by-step explanation:

For statement 2, we use segment addition postulate to say AC= AE+EC.

Answer 2

Geometry proofs can be used to show that the congruence of line segments.

The complete statements and reasons ate:

1. $AE = BD;\ CD = CE$ --- Given
2. $AE = AC + CE$ ----- Segment addition postulate
3. $BD = AC + CD$ ----- Substitution property of equality
4. $AC + CD = BD$ ---- Segment Addition Postulate
5. $AC+CD=BC+CD$ ---- Transitive property of equality
6. $AC = BC$ --- Subtraction property of equality.

Step 1

The given parameters from the question are:

$AE = BD;\ CD = CE$

Step 2

We have:

$AE = AC + CE$

The above represents segment addition postulate, because point C is on line segment AE

Step 3

Substitute BD for AE and CD for CE in $BD= AC + CD$

$BD = AC + CD$

The above represents substitution property of equality

Step 4

In step 3, we have:

$BD = AC + CD$

Apply symmetric property of equality

$AC + CD = BD$

Step 5

Point C is on line segment BD.

So, we have:

$BD= BC+CD$

The above represents segment addition postulate

Step 6

Transitive property states that:

If $a = b,\ b = c$, then $a = c$

So, we have:

$AC+CD=BC+CD$

This is so, because:

$AC + CD = BC + CD = BD$

Step 7

Subtract CD from both sides of $AC+CD=BC+CD$

$AC = BC$

The above statement represents subtraction property of equality.

Read more about geometry proof at:

https://brainly.com/question/1601567