Two column proof
Given:kl=kj and gj= hl
prove: GLJ =HJL
Photo is basically a box with an X in it.
G----------------------H
|\ / |
| \ K / |
| \ / |
| / \ |
L ------/------\------ J
KG = KH ..... HL-KL = GJ-KJ (subtraction of equals)
m∠GKL = m∠HKJ ......... vertical angles
∆GKL ≅ ∆HKJ .......... SAS
m∠GLJ = m∠HJL ............. CPCTC
To prove that GLJ = HJL, we can use a two-column proof. Here's how we can approach it:
Statement | Reason
---------|-------
kl = kj | Given
gj = hl | Given
???? = ???? | Something to be determined
GLJ = HJL | What we need to prove
To find the missing step, we can start by looking at the given information. We have kl = kj and gj = hl. Notice that the k and h terms appear on both sides, so we can focus on those.
We can consider the possibility of using the Transitive Property of Equality to connect the two sets of congruent sides.
By the Transitive Property of Equality, if kl = kj and gj = hl, then it's possible to say that kl = hl. We can then fill in this information in the missing step in our proof:
Statement | Reason
---------|-------
kl = kj | Given
gj = hl | Given
kl = hl | Transitive Property of Equality
GLJ = HJL | ?
Now, to show that GLJ = HJL, we can focus on the gj = hl relationship. Since gj = hl, we have a pair of congruent angles. Therefore, we can use the Vertical Angles Theorem, which states that vertical angles are congruent. In this case, gj and hl are vertical angles, so we can write GLJ = HJL in the proof:
Statement | Reason
---------|-------
kl = kj | Given
gj = hl | Given
kl = hl | Transitive Property of Equality
GLJ = HJL | Vertical Angles Theorem
By establishing the congruency of the corresponding sides and the congruency of the vertical angles, we have successfully proven that GLJ = HJL.