Question

2. В треугольнике ABC AB = BC, K - середина отрезка АС. На сторонах AB и ВС выбраны точки Е и Р соответственно так, что угол AKE = углу CKP. Докажите, что треугольник AKE= треугольнику CKP.​

Answer 1

Объяснение:

Тр-к АКЕ и тр-к СКР

<А=<С - по условию, т. к АВ=ВС, тр-к АВС равнобедренный.

АК=СК - по условию, т. к К - середина АС

<АКЕ=<СКР - по условию

Тр-к АКЕ= тр-ку СКР по стороне и двум прилежащим углам ( по 2 признаку)

Answer 2

Given Information:

We are given a triangle ABC, where AB = BC. K is the midpoint of segment AC. Points E and P are chosen on sides AB and BC, respectively, such that angle AKE is equal to angle CKP. We need to prove that triangle AKE is congruent to triangle CKP.

Proof:

To prove that triangle AKE is congruent to triangle CKP, we can use the Side-Angle-Side (SAS) congruence criterion.

1. Side AE is congruent to side CP: - Since K is the midpoint of AC, we can use the Midpoint Theorem to conclude that AK is congruent to KC. - Given that AB = BC, we can also conclude that AE is congruent to CP. - Therefore, side AE is congruent to side CP.

2. Angle AKE is congruent to angle CKP: - It is given that angle AKE is equal to angle CKP. - Therefore, angle AKE is congruent to angle CKP.

3. Side AK is congruent to side KP: - From the Midpoint Theorem, we know that AK is congruent to KC. - Since angle AKE is congruent to angle CKP, we can conclude that triangle AKE is congruent to triangle CKP by the SAS congruence criterion.

Therefore, triangle AKE is congruent to triangle CKP.

Note: The proof assumes that the given information is correct and that the angles and sides mentioned are well-defined and measurable.