Geometry-Deductive Reasoning & Proofs.

[KSmid13]

Hi, I did my homework from last night, but i dont understand it at all. The ones in bold are the ones that im not sure of & would like checked over, but if theres time just skim over the rest.
This is only one section of my homework, but i cant post the rest because theres angles that need to be shown inorder to answer the problem. But, if you have any advice on learning about this, or proofs, please let me know.
Thanks for your help.

Name the property that justifies each statement.
1. Angle Z is congruent to Angle Z
-My answer: Reflexsive Property of Congruence.
:?: 2. If 12x = 84, then x = 7
-My answer: Given. *im not sure of this.
3. If segment ST is congruent to segment QR, then segment QR is congruent to segment ST
-My answer: Transition Property of Congruence.
4. IF 3x+14 = 80, then 3x = 66
-My answer: Addition Property of Equality.
5. If 2x+y=5 and x=y, then 2x+x=5
-My answer: Subtraction Property of Equality.
:?: 6. If AB-BC=12, then AB=12+BC
-My answer: Subtraction Property of Equality. *im not sure of this.
7. If the measurement of angle A =15, then 3(the measurement of angle A=45
-My answer: Multiplication Property of Equality.
8. QR=QR
-My answer: Reflexsive Property of Equality.
9. If Angle 1 is congruent to Angle 2 and Angle 2 is congruent to Angle 3, then Angle 1 is congruent to Angle 3.
-My answer: Reflexsive Property of Equality.
10. 2(3x+5)=6x+10
-My answer: Subsitituion Property of Equality.

 

[soroban]

Hello, KSmid13!

"Equality" and "congruence" mean the same thing,
. . but did you mean to swtich back and forth?

Name the property that justifies each statement.

$\displaystyle \text{1. Angle }Z\text{ is congruent to angle }Z.$
- My answer: Reflexive Property of Equality. . Right!

$\displaystyle \text{2. If }12x = 84\text{, then }x = 7$

Both sides were divided by 12.

It must be "Division Property of Equality."

$\displaystyle \text{3. If }ST = QR\text{, then }QR = ST$
- My answer: Transition Property of Congruence. . no

Note that the two sides are "switched".

This is the "Symmetric Property of Equality."

$\displaystyle \text{4. If } 3x+14 = 80\text{, then }3x = 66$
- My answer: Addition Property of Equality . no

Note that 14 is subtracted from both sides.

This is the "Subtraction Property of Equality".

$\displaystyle \text{5. If }2x+y=5\text{ and }x=y\text{, then }2x+x=5$
- My answer: Subtraction Property of Equality . no

$\displaystyle \text{Going from }\,2x+y\,=\,5\,\text{ to }\,2x+x\,=\,5$
. . $\displaystyle y\text{ was replaced by }x.$

This is the "Substitution Property."

$\displaystyle \text{6. If }AB-BC\,=\,12\text{, then }AB\,=\,12+BC$
- My answer: Subtraction Property of Equality . no

Note that $\displaystyle BC$ was added to both sides.

This is the "Addition Property of Equality".

$\displaystyle \text{7. If (measurement of angle A)}\,=\,15\text{, then 3(measurement of angle A)}\,=\,45$
- My answer: Multiplication Property of Equality . Yes!

$\displaystyle \text{8. }QR\,=\,QR$
- My answer: Reflexive Property of Equality . Correct!

\(\displaystyle \text}9. If }\angle 1\,=\,\angle 2\,\text{ and }\,\angle 2\,=\,\angle 3\text{, then }\angle 1\,=\,\angle 3\)
- My answer: Reflexive Property of Equality . no

(How can this be the same as #8 ?)

This is the "Transitive Property of Equality".

$\displaystyle 10.\;2(3x+5)\:=\:6x+10$
- My answer: Subsitituion Property of Equality . no

They "multiplied through by the 2".

This is the "Distributive Property".