Wiki Exercise 8. Exchange the bold typed words by pronouns.
e.g: Pete lives here. I saw Pete yesterday. He lives here. I saw him yesterda
1. Alice is my girlfriend. I love Alice.
2. Jane and I saw Mark but Mark did not see Jane and me.
3. I told Steve and Carol to come to me.
4. My parents liked the cat and I bought the cat.
5. Why are the books on the table? Put the books on the shelf.
6. It is a nice bird. Listen how lovely the bird is singing.
7. Your friend and you are late again.
8. My sister and I are great friends.
9. I haven't seen Pete and Alex today.
10. Steve and Mark have invited my friend and me to the cinema.​

Дано:

<AOB и <COD

<COD  внутри <AOB 

AO ┴ OD;  CO ┴ OB;

<AOB - <COD = 90°

Найти: <AOB и <COD.

Решение

Т.к . AO ┴ OD;  CO ┴ OB,

то <AOD = 90; <COB = 90°.

 <COD = <AOD  - <AOC

<COD = <COB  - <DOB

<COD = 90° - <AOC

<COD = 90° - <DOB

Получим

<AOC = 90° - <COD

<DOB = 90° - <COD

Следовательно <AOC = <DOB

2) По условию: <AOB - <COD = 90°

Но если от всего угла  <AOB отнять <COD, то останутся два равных угла  <AOC и <DOB, значит, это их сумма равна 90°.

<AOC + <DOB = 90° =>

<AOC = <DOB = 90°/2 = 45°

3) <COD = 90° - <DOB

<COD = 90° - 45°=45°

4) <AOB = <AOC + <DOB + <DOB

<AOB = 45° + 45° + 45° = 135°

ответ: <AOB - 135°;  <COD =45°.

В треугольнике ABC с угла B Проведена прямая BD. Найдите отношение P(∆BDC)/P(∆ABC), если ∠ABC=∠BDC, AB=8, AC=12, DC=3. Надо найти сторону BD и периметры ∆ ABC и ∆ BDC ​.

ответ: 1 : 2 , 4 , 26 , 13 .

Объяснение:

ΔCDB ~ ΔCBA ( по первому признаку подобия) и почти конец

∠BDC= ∠ABC ← условие

∠C _общий угол

BC/AC =DC/BC = BD / AB =P(∆BDC)/P(∆ABC)

BC² =AC *DC=12*3 =36 ⇒ BC=6 ; P(∆BDC)/P(∆ABC) =BC/AC=6/12 =1: 2

BC/AC = BD / AB ⇒ BD =(BC/AC)*ABС =(6/12)*8 = 4 ;

P(∆ ABC) =AB++AC+BC =8+12+6 =26 ;

P(∆BDC) = (1/2)*P(∆ABC) =(1/2)*26 =13 или 3+4+6 =13 .