To prove that LO = MN in isosceles triangle KLM where KL = KM and KN = KO, you can use the following steps:
1. Draw triangle KLM with KL = KM and KN = KO.
2. Since triangle KLM is isosceles, angle KLM = angle KML (base angles are congruent).
3. Now, consider triangle KLN and triangle KMO.
4. By the Angle-Side-Angle (ASA) congruence criterion, you can conclude that triangle KLN is congruent to triangle KMO because:
- Angle KLN = angle KMO (by step 2).
- KN = KO (given).
- KL = KM (given).
5. When two triangles are congruent, their corresponding sides are also congruent. Therefore, LO = MN, since they are corresponding sides of congruent triangles KLN and KMO.
To prove that LO MN in isosceles triangle KLM where KL = KM and KN = KO, you can use the following steps:
1. Draw triangle KLM with KL = KM and KN = KO.
2. Since triangle KLM is isosceles, angle KLM = angle KML (base angles are congruent).
3. Now, consider triangle KLN and triangle
KMO.
4. By the Angle-Side-Angle (ASA)
congruence criterion, you can conclude that triangle KLN is congruent to triangle KMO because:
- Angle KLN = angle KMO (by step 2).
- KN = KO (given).
- KL = KM (given).
5. When two triangles are congruent, their corresponding sides are also congruent. Therefore, LO MN, since they are corresponding sides of congruent triangles KLN and KMO.
This proves that LO = MN in triangle KLM. [tex][/tex]
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Answer:
To prove that LO = MN in isosceles triangle KLM where KL = KM and KN = KO, you can use the following steps:
1. Draw triangle KLM with KL = KM and KN = KO.
2. Since triangle KLM is isosceles, angle KLM = angle KML (base angles are congruent).
3. Now, consider triangle KLN and triangle KMO.
4. By the Angle-Side-Angle (ASA) congruence criterion, you can conclude that triangle KLN is congruent to triangle KMO because:
- Angle KLN = angle KMO (by step 2).
- KN = KO (given).
- KL = KM (given).
5. When two triangles are congruent, their corresponding sides are also congruent. Therefore, LO = MN, since they are corresponding sides of congruent triangles KLN and KMO.
This proves that LO = MN in triangle KLM.
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To prove that LO MN in isosceles triangle KLM where KL = KM and KN = KO, you can use the following steps:
1. Draw triangle KLM with KL = KM and KN = KO.
2. Since triangle KLM is isosceles, angle KLM = angle KML (base angles are congruent).
3. Now, consider triangle KLN and triangle
KMO.
4. By the Angle-Side-Angle (ASA)
congruence criterion, you can conclude that triangle KLN is congruent to triangle KMO because:
- Angle KLN = angle KMO (by step 2).
- KN = KO (given).
- KL = KM (given).
5. When two triangles are congruent, their corresponding sides are also congruent. Therefore, LO MN, since they are corresponding sides of congruent triangles KLN and KMO.
This proves that LO = MN in triangle KLM. [tex][/tex]