Question

точки A и B лежат по разные стороны от прямой KM, AK ll BM, AK=BM.докажи что треугольник AK=треугольнику BM и найди длину AM, если MB =8 , а KB=12 . СРОЧНОООО ДАМ 35 БАЛЛОВ!

Answer 1

Точки A и B лежат по разные стороны от прямой KM, AK ll BM, AK=BM. Докажи, что треугольник AKМ равен треугольнику BКM и найди длину

AM, если MB =8 , а KB=12

Ответ:

АМ=12 ед

Объяснение:

1)△КАМ = △МВК по двум сторонам и углу между ними (первый признак равенства треугольников):

• КМ - общая
• ∠АКМ=∠ВМК - как внутренние накрест лежащие углы при параллельных прямых АК и ВМ и секущей КМ
• АК=ВМ - по условию.

2) Из равенства треугольников следует равенство сторон: АМ=КВ=12см.

Answer 2

Given Information

The points A and B lie on opposite sides of the line KM, and AK is parallel to BM with AK = BM.

Proof of Triangle AKM ≅ Triangle BKM

To prove that triangle AKM is congruent to triangle BKM, we can use the fact that they share a common side KM and have equal corresponding sides AK and BM.

By the definition of congruent triangles, if two triangles have the same three sides, then they are congruent. Given that AK = BM and AK is parallel to BM, we can conclude that triangle AKM is congruent to triangle BKM by the Side-Side-Side (SSS) congruence criterion.

Proof: 1. AK = BM (Given) 2. AK || BM (Given) 3. KM is common to both triangles 4. By SSS criterion, triangle AKM ≅ triangle BKM

Finding the Length of AM

Given that MB = 8 and KB = 12, we can find the length of AM using the fact that AK = BM.

Since AK = BM, we can consider the triangle AKM as an isosceles triangle, where AM is the base and KM is the equal side.

Using the property of isosceles triangles, the length of the base (AM) can be calculated using the formula: AM = √(2 * (AK^2) - (KM^2))

Substituting the given values: AK = BM = 8 KM = 12

AM = √(2 * (8^2) - (12^2)) = √(128 - 144) = √(-16) = 4i

Therefore, the length of AM is 4i.

In this context, "i" represents the imaginary unit, indicating that the length of AM is a complex number.

I hope this helps! If you have further questions or need additional assistance, feel free to ask.