Consider parallel lines cut by a transversal. Explain which theorems, definitions, or combinations of both can be used to prove
that alternate exterior angles are congruent.
2 answers:
Answer:
Corresponding angle theorem, vertical angle theorem, and the transitive property of congruence.
Step-by-step explanation:
In the context of parallel lines intersected by a transversal. (Refer to the attached image).
Given that lines J and K are parallel, according to "corresponding angle theorem"
By "vertical angle theorem"
Utilizing "transitive property of congruence"
Thus, this forms our needed proof. Throughout this proof, we incorporated the "corresponding angle theorem,” “vertical angle theorem,” and the "transitive property of congruence."
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Answer:
Upon solving for y, we find:
By substitution, we have:
Thus, we arrive at:
And for x, we determine:
This gives us a length of 76 and a width of 12.5.
Step-by-step explanation:
We are dealing with a rectangle. The formula for the perimeter is:
Here, x denotes the length and y the width. The following conditions can be established:
Substituting these values yields:
When we solve for y, we find:
By substitution, we obtain:
Thus, we conclude:
The length is found to be 76, while the width measures 12.5.