Question

Добоможіть! 100 Баллов! Потрібно користуватися операціями, що називаються елементарними побудовами, а розв’язати задачу на побудову! 1.Побудуйте гострий кут. За допомогою циркуля і лінійки побудуйте кут, що дорівнює даному та його бісектрису. 2.Дано відрізки: SE = 4 см, EF = 5 см і SF = 8 см. За допомогою циркуля і лінійки побудуйте трикутник SEF. 3.Дано відрізки СА = 4 см і СВ = 3 см. За допомогою циркуля та лінійки побудуйте прямокутний трикутник, катети якого дорівнюють відрізкам СА і СВ.

Answer 1

Ответ:

в фото

1

Пряму переносимо циркулем. Проводимо дугу циркулем на куту А та такуж саму на куті В. Відміряємо відстань дуги та переносимо. Потім проводимо круги від країв дуги у куті В місце їх перетину буде місце через яке проходить бісектриса.

2

Будуємо відрізок SFз обох кінців проводимо циркулем півкруги радіуси яких 5 і 4, До точки перетину проводимо відрізки.

3

Малюемо один з катетів а інший переносимо циркулем під кутом 90 з'єднуємо відрізки та отримуємо прямокутний трикутник

Answer 2

Task 1: Constructing an acute angle and its bisector

To construct an acute angle and its bisector, you can follow these steps:

1. Draw a line segment AB using a ruler. 2. Place the center of the compass at point A and draw an arc that intersects line AB. 3. Without changing the compass width, place the center of the compass at point B and draw another arc that intersects the previous arc. 4. Label the points of intersection as C and D. 5. Draw a line segment through points A and C, and another line segment through points A and D. 6. The angle formed by lines AC and AD is the acute angle you constructed. 7. To construct the bisector of the angle, place the compass center at point A and draw an arc that intersects both lines AC and AD. 8. Without changing the compass width, place the compass center at the point of intersection of the arcs and draw another arc. 9. Label the point of intersection as E. 10. Draw a line segment through points A and E. 11. The line segment AE is the bisector of the acute angle.

Please note that the specific measurements or angles required for this task are not provided. You can adjust the lengths of the line segments and the angle as needed.

Task 2: Constructing a triangle with given line segments

To construct a triangle with given line segments, you can follow these steps:

1. Draw a line segment EF using a ruler. 2. Place the center of the compass at point E and draw an arc that intersects line EF. 3. Without changing the compass width, place the center of the compass at point F and draw another arc that intersects the previous arc. 4. Label the points of intersection as S and G. 5. Draw a line segment through points S and G. 6. Label the point of intersection between line segment SG and line segment EF as H. 7. Draw a line segment through points E and H. 8. Draw a line segment through points F and H. 9. The triangle SEF is the triangle you constructed using the given line segments.

Please note that the specific measurements of the line segments SE, EF, and SF are provided as 4 cm, 5 cm, and 8 cm, respectively. Adjust the lengths of the line segments accordingly.

Task 3: Constructing a right triangle with given line segments

To construct a right triangle with given line segments, you can follow these steps:

1. Draw a line segment CA using a ruler. 2. Draw a line segment CB using a ruler. 3. Place the center of the compass at point C and draw an arc that intersects line segment CA. 4. Without changing the compass width, place the center of the compass at point C and draw another arc that intersects line segment CB. 5. Label the points of intersection as D and E. 6. Draw a line segment through points D and E. 7. The triangle CDE is the right triangle you constructed using the given line segments.

Please note that the specific measurements of the line segments CA and CB are provided as 4 cm and 3 cm, respectively. Adjust the lengths of the line segments accordingly.

I hope this helps! Let me know if you have any further questions.