1)given-AB=CD,CD=EF
prove-AB-EF (in 5 steps that show why it is corect; i.e two-column proof)
2)Given-<2=<3, <4=<5
prove-<1 is supplementay to <6
(in 3 steps, with the two column proof)
TWO-COLUMN PROOF LOOKS LIKE THIS....
STATEMENT: REASON:
1.AB=CD,CD=EF 1.Given
2.?? 2.??
3.?? 3.??
4.?? 4.??
5.AB=EF 5.??
Transitive Axiom If a = b and b = c then a = c
So it seems to me to be two steps, not five.
You second makes no sense, it does not indicate any relationship with <1 and any other angle.
Purple because aliens dont wear hats
wth does that mean
I am also having issues with that given, but I'm not sure if its the same...
Given: AB = CD, CD = EF
Prove: AB = EF
Statement: Reason:
1. AB ≅ CD Given
2. _______ Definition of Congruence
3. CD ≅ EF ___________________
4. CD = EF ___________________
5. AB = EF ___________________
6. _______ Definition of Congruence
This is one of the questions and whatever in my assignment, and I'm having some issues in solving it. So, if anyone knows pls help. Thank you.
To prove AB = EF given AB = CD and CD = EF, you can follow these steps in a two-column proof:
1. AB = CD, CD = EF Given
2. AB = AB + CD Addition Property of Equality (Adding the same value to both sides of an equation)
3. AB + CD = EF + CD Substitution Property of Equality (Substituting CD with its equivalent EF)
4. AB + CD = EF Transitive Property of Equality (Since CD = EF and AB = CD, then AB = EF)
5. AB = EF Symmetric Property of Equality (Since AB = EF, then EF = AB)
The completed two-column proof would look like this:
Statement Reason
1. AB = CD, CD = EF Given
2. AB = AB + CD Addition Property of Equality
3. AB + CD = EF + CD Substitution Property of Equality
4. AB + CD = EF Transitive Property of Equality
5. AB = EF Symmetric Property of Equality
Now, let's move on to the second question:
To prove <1 is supplementary to <6 given <2 = <3 and <4 = <5, you can follow these steps in a two-column proof:
1. <2 = <3, <4 = <5 Given
2. <2 + <4 = <3 + <4 Addition Property of Equality (Adding the same value to both sides of an equation)
3. <2 + <4 = <6 Substitution Property of Equality (Substituting <5 with its equivalent <6)
4. <1 + <6 = <2 + <4 Transitive Property of Equality (Since <2 + <4 = <6 and <1 + <6 = <1 + <6, then <1 + <6 = <2 + <4)
5. <1 + <6 = 180° Definition of Supplementary Angles (Supplementary angles add up to 180 degrees)
The completed two-column proof would look like this:
Statement Reason
1. <2 = <3, <4 = <5 Given
2. <2 + <4 = <3 + <4 Addition Property of Equality
3. <2 + <4 = <6 Substitution Property of Equality
4. <1 + <6 = <2 + <4 Transitive Property of Equality
5. <1 + <6 = 180° Definition of Supplementary Angles.