Line segment + geometry construction - practice problems
Number of problems found: 29
- Half-planes 36831
The line p and the two inner points of one of the half-planes determined by the line p are given. Find point X on the line p so that the sum of its distances from points A and B is the smallest.
- Extreme 5456
Draw line AB if you know one of its extreme points and the center of line S.
- Three points
Mark three points E, F, and G in the plane, not lie on one line. a) Draw a line segment FG b) Construct halfline (ray) EG c) Draw a line EF
- Pieces 6890
Divide the line MN (/ MN / = 9cm) into 11 equal pieces
- Square ABCD
Construct a square ABCD with center S [3,2] and the side a = 4 cm. Point A lies on the x-axis. Construct a square image in the displacement given by oriented segment SS'; S` [-1 - 4].
- Intersection 7247
On side AB of triangle ABC, points D and E are given such that |AD| = |DE| = |EB|. Points A and B are the midpoints of segments CF and CG. Line CD intersects line FB at point I, and line CE intersects line AG at point J. Prove that the intersection of lin
- Sides of the triangle
The sides of the triangle ABC have a length of 4 cm, 5 cm, and 7 cm. Construct triangle A'B'C', similar to triangle ABC, which has a circumference of 12 cm.
- Simultaneously 5010
Construct the circles k1 (S1;r1) and k2(S2;r2), if S1 S2 = 7 cm, d1= 12 cm and r2 = 1/2 r1. Mark the point: a) A lying on circle k1, b) B lying in both circles determined by circles k1 and k2, c) C lying simultaneously on both circles, d) D, for which: (S
- Reduction 33021
Draw the line AB = 14 cm and divide it by the reduction angle in the ratio of 2:9.
- Connect 6500
Draw the line KL = 55mm. Draw a circle k with center K and a radius of 4cm. Mark the points to belong to the circle and connect them with point L.
- Department 4220
Draw the line segment AB, AB = 5 cm. Draw a set of points 2 cm away from line AB. What is the district's department?
- Outside tangents
Calculate the length of the line segment S1S2 if the circles k1 (S1, 8cm) and k2 (S2,4cm) touch the outside.
- Mrak - cloud
It is given segment AB, which is 12 cm in length, on which one side of the square MRAK is laid. MRAK's side length is 2 cm shown. MRAK gradually flips along the line segment AB, and point R leaves a paper trail. Draw the whole track of point R until the s
- Hypotenuse - construct problem
A line segment AA1 of length 6 cm is given. Construct all triangles ABC for which AA1 is the hypotenuse, side length BC is 5 cm, and angle gamma is 60°.
- Hypotenuse 78844
Construct triangle KLM if side m=6.5cm, hypotenuse tm=4cm, height to side m: vm=3.2cm
- Rhombus construction
Construct ABCD rhombus if its diagonal AC=9 cm and side AB = 6 cm. Inscribe a circle in it, touching all sides.
- Trisection of a line segment
Divide the line segment AB into three equal parts. Instructions: Construct an equilateral triangle ABC and find its center (e.g., the described circles).
- Katy MO
Kate drew a triangle ABC. The middle of the line segment AB is marked as X, and the center of the side AC is marked as Y. On the side BC, she wants to find point Z so that the area of a 4gon AXZY is the greatest. What part of the ABC triangle can maximall
- Hypotenuse 65744
Construct a right triangle ABC with the hypotenuse AB: a) | AB | = 72 mm, | BC | = 51 mm b) | AB | = 58 mm, | AC | = 42 mm
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