Question

Дано: АВСД параллелограмм. ВЕ биссектриса = 2 см. Угол СВЕ= 60 градусов. АВ= 10 см. Найти АД и ДС!

Answer 1

∠СВЕ=∠АВЕ=60°.
∠АВЕ=∠ВЕС как накрест лежащие при параллельных АВ и СД и секущей ВЕ, значит ∠СВЕ=∠ВЕС=60°, значит тр-ник ВЕС равносторонний, значит ВС=ВЕ=2 см.
В параллелограмме АВСД АД=ВС=2 см, ДС=АВ=10 см - это ответ.

Answer 2

Solution for Finding AD and DS in Parallelogram ABCD

To find the lengths of AD and DS in parallelogram ABCD, we can use the properties of a parallelogram and the given information about the bisector VE and angle SVE.

1. Using Properties of a Parallelogram: - In a parallelogram, opposite sides are equal in length.

2. Using Given Information: - VE is a bisector, so it divides side AD into two equal parts. - Angle SVE is given as 60 degrees.

Calculation Steps:

1. Finding AD: - Since VE bisects AD, we can find the length of AD by using the properties of a parallelogram and the given information.

- Let's denote the length of AD as x. - Since VE bisects AD, both parts of AD are equal, so AD = 2x. - Using the given information that AB = 10 cm, we can find x.

2. Finding DS: - Since ABCD is a parallelogram, AD = BC and AB = DC. - We can use the given information about AB to find the length of DC. - Then, we can find the length of DS using the properties of a parallelogram.

Final Results:

1. Length of AD: - We will calculate the length of AD using the given information and properties of a parallelogram.

2. Length of DS: - We will calculate the length of DS using the properties of a parallelogram and the length of AD.

Let's proceed with the calculations.