Question

От вершины М равнобедренного треугольника KLM(MK=ML) отложены равные отрезки: MN на стороне MK и MH на стороне M. Докажите, что угол MKH = углуMLNпомогите. очень нужно! за ранее большое спасибо)

Answer 1

Треугольник KNH РАВЕН треугольнику LHN по трем сторонам. 
1. Сторона NH общая 
2. NK = HL т. к. на равных сторонах (равнобедренный тр-к) отложили равные отрезки 
3. NH || KL, получилась равнобокая трапеция, ее диагонали равны. => KH = NL 

У равных треугольников соответствующие углы равны. 
< NKH = < HLN 

< MKH = < MLN

Answer 2

To prove that angle MKH is equal to angle MLN, we can use the properties of isosceles triangles and the fact that corresponding angles of congruent triangles are equal.

Given Information:

- Triangle KLM is an isosceles triangle with MK = ML. - MN is a segment on side MK. - MH is a segment on side ML.

Proof:

1. Since triangle KLM is isosceles with MK = ML, we know that angles KML and KLM are congruent. 2. By the properties of isosceles triangles, we also know that angles MKL and MLK are congruent. 3. Since MK = ML, triangle MKL is an isosceles triangle. 4. Therefore, angles MKL and MLK are congruent. 5. Since angles KML and KLM are congruent, and angles MKL and MLK are congruent, we can conclude that triangle MKL is an isosceles triangle with congruent base angles. 6. By the properties of isosceles triangles, we know that the angles opposite the congruent sides are congruent. 7. Therefore, angle MKH is congruent to angle MLN, as they are opposite the congruent sides MN and MH, respectively.

Hence, we have proved that angle MKH is equal to angle MLN.

Please let me know if you need any further clarification or assistance!