Reason + geometry construction - practice problems
Number of problems found: 17
- Parallelogram 80761
Construct a parallelogram ABCD if a=5 cm, height to side a is 5 cm, and angle ASB = 120 degrees. S is the intersection of the diagonals. - Circumscribing 80498
Given is an acute-angled triangle ABC. On the half lines opposite to BA and CA lie successively the points D and E such that |BD| = |AC| and |CE| = |AB|. Prove that the center of the circle circumscribing triangle ADE lies on the circle circumscribing tri - Shortest walk
An ant is crawling around this cube. The cube is made of wire. Each side of the cube is 3 inches long. (Those sides are called edges.) Points A and B are vertices of the cube. What is the least distance the ant would have to crawl if it starts from point - Symmetrical 67454
How many more squares in the grid in the picture need to be painted to make it centrally symmetrical? square - x x; o; o; x o; o; x; o x; o; o; o o; x; o; o This is a sketch of a grid where the colored squares are x. Thank you, Lucy
- (perimeter) 61854
Construct triangle ABC when we know a + b + c (perimeter), height to side c, and angle gamma. - Center-symmetric 58201
Find out which we can write letters (uppercase) as center-symmetric. - Construction 55311
Construct a KLM triangle where side k is 6.7 cm, the line to the k side is 4.1 cm, and the LKM angle is 63 degrees. Write the construction procedure. - Divide an isosceles triangle
How to divide an isosceles triangle into two parts with equal areas perpendicular to the axis of symmetry (into a trapezoid and a triangle)? - Triangle 35881
The sum of the lengths of the two sides b + c = 12 cm Beta angle = 68 Gamma angle = 42 draw triangle ABC
- Construct 10921
Construct the diamond ABCD so that its diagonal BD is 8 cm and the distance of apex B from the line AD is 5 cm. Specify all options - 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 - Triangles
Ivo wants to draw all the triangles whose two sides of which have a length of 4 cm and 9 cm, and the length of the third side is expressed in whole centimeters. How many triangles does he have? - Perpendicular 5865
We cut the cube with two mutually perpendicular cuts, each parallel to one of the cube's walls. By what percentage is the sum of the surfaces of all cuboids created in this way greater than the surface of the original cube? - Intersect 5216
At how many points do ten lines intersect if no two are parallel?
- Hypotenuse 4221
Find the set of points formed by the center of gravity of right triangles with the same hypotenuse (build several possible triangles into one image). - Z9–I–1
In all nine fields of given shape to be filled with natural numbers so that: • each of the numbers 2, 4, 6, and 8 is used at least once, • four of the inner square boxes containing the products of the numbers of adjacent cells of the outer square, • in th - Hexagon = 8 parts
Divide the regular hexagon into eight equal parts.
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