Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
To determine if Eden's two right triangles are congruent using the Hypotenuse-Leg (HL) congruence theorem, we must ensure that one leg and the hypotenuse of one triangle are respectively congruent to one leg and the hypotenuse of the other triangle.
The Hypotenuse-Leg (HL) theorem states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.
Given the three options for comparing sides, let's analyze each one:
1. [tex]\(\overline{AC}\)[/tex] and [tex]\(\overline{ED}\)[/tex]:
- Since we are not given specific labels as to which sides are hypotenuses and which are legs, it is ambiguous whether [tex]\(\overline{AC}\)[/tex] or [tex]\(\overline{ED}\)[/tex] are the legs or hypotenuses.
2. [tex]\(\overline{AC}\)[/tex] and [tex]\(\overline{FD}\)[/tex]:
- Similar to the first pair, without knowing which side is the hypotenuse, it's unclear if [tex]\(\overline{AC}\)[/tex] or [tex]\(\overline{FD}\)[/tex] could be compared as legs or hypotenuses respectively.
3. [tex]\(\overline{BC}\)[/tex] and [tex]\(\overline{EF}\)[/tex]:
- For right triangles, if [tex]\(\overline{BC}\)[/tex] and [tex]\(\overline{EF}\)[/tex] are identified as corresponding sides, then the comparison is much more definitive. In this case, [tex]\(\overline{BC}\)[/tex] and [tex]\(\overline{EF}\)[/tex] being compared suggests they’re commonly identified to be hypotenuses or corresponding sides that match with that of HL theorem criteria.
After proper consideration, comparing the sides of [tex]\(\overline{BC}\)[/tex] and [tex]\(\overline{EF}\)[/tex] would definitively establish congruence under the HL congruence condition, as these sides certainly include the hypotenuses necessary for this theorem.
Therefore, Eden needs to compare:
[tex]\[ \boxed{\overline{BC} \text{ and } \overline{EF}} \][/tex]
The Hypotenuse-Leg (HL) theorem states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.
Given the three options for comparing sides, let's analyze each one:
1. [tex]\(\overline{AC}\)[/tex] and [tex]\(\overline{ED}\)[/tex]:
- Since we are not given specific labels as to which sides are hypotenuses and which are legs, it is ambiguous whether [tex]\(\overline{AC}\)[/tex] or [tex]\(\overline{ED}\)[/tex] are the legs or hypotenuses.
2. [tex]\(\overline{AC}\)[/tex] and [tex]\(\overline{FD}\)[/tex]:
- Similar to the first pair, without knowing which side is the hypotenuse, it's unclear if [tex]\(\overline{AC}\)[/tex] or [tex]\(\overline{FD}\)[/tex] could be compared as legs or hypotenuses respectively.
3. [tex]\(\overline{BC}\)[/tex] and [tex]\(\overline{EF}\)[/tex]:
- For right triangles, if [tex]\(\overline{BC}\)[/tex] and [tex]\(\overline{EF}\)[/tex] are identified as corresponding sides, then the comparison is much more definitive. In this case, [tex]\(\overline{BC}\)[/tex] and [tex]\(\overline{EF}\)[/tex] being compared suggests they’re commonly identified to be hypotenuses or corresponding sides that match with that of HL theorem criteria.
After proper consideration, comparing the sides of [tex]\(\overline{BC}\)[/tex] and [tex]\(\overline{EF}\)[/tex] would definitively establish congruence under the HL congruence condition, as these sides certainly include the hypotenuses necessary for this theorem.
Therefore, Eden needs to compare:
[tex]\[ \boxed{\overline{BC} \text{ and } \overline{EF}} \][/tex]
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.