Geometry construction problems - examples
- Katy MO
Kate draw triangle ABC. Middle of AB have mark as X and the center of the side AC as Y. On the side BC wants to find the point Z such that the content area of a 4gon AXZY was greatest. What part of the triangle ABC can maximally occupy 4-gon AXZY?
In all nine fields of given shape to be filled 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 the cir
- Square grid
Square grid consists of a square with sides of length 1 cm. Draw in it at least three different patterns such that each had a content of 6 cm2 and circumference 12 cm and that their sides is in square grid.
- Diagonal in rectangle
In that rectangle ABCD is the center of BC point E and point F is center of CD. Prove that the lines AE and AF divide diagonal BD into three equal parts.
- Isosceles - isosceles
It is given a triangle ABC with sides /AB/ = 3 cm /BC/ = 10 cm, and the angle ABC = 120°. Draw all points X such that true that BCX triangle is an isosceles and triangle ABX is isosceles with the base AB.
Draw a square on the edge of a = 4 cm. Mark the center of symmetry S and all axes of symmetry. How many axes of symmetry does? Write down.
- Mrak - cloud
It is given segment AB of length 12 cm, where one side of the square MRAK laid on it. MRAK's side length 2 cm shown. MRAK gradually flips along the line segment AB the point R leaves a paper trail. Draw the whole track of point R until square can do the.
- Construct 1
Construct a triangle ABC, a = 7 cm, b = 9 cm with right angle at C, construct the axis of all three sides. Measure the length of side c (and write).
- Circle tangent
It is given to a circle with the center S and radius 3.5 cm. Distance from the center to line p is 6 cm. Construct a circle tangent n which is perpendicular to the line p.
Draw a rectangle with the sides a = 4 cm, b = 5 cm. Mark the center of symmetry S and all axes of symmetry. How many axes of symmetry has? Write down.
- Tangents construct
Circle is given k (S; 2.5 cm) and an outer line p. Construct a tangent t of the circle that has with a line p angle 60°. How many solutions has the task?
- Sides od triangle
Sides of the triangle ABC has length 4 cm, 5 cm and 7 cm. Construct triangle A'B'C' that are similar to triangle ABC which has a circumference of 12 cm.
Draw a square ABCD whose diagonals have a length of 6 cm
- Outer contact of circles
Construct a circle k1 (S1; 1.5 cm), k2 (S2; 2 cm), and K3 (S3; 2.5 cm) so that they are always two outer contact. Calculate the perimeter of the triangle S1S2S3.
- Hexagon = 8 parts
Divide the regular hexagon into eight equal parts.
- Triangle SSA
Construct a triangle ABC if |AB| = 5cm va = 3cm, CAB = 50 °. It is to create the analysis and construction steps.
- Complete construction
Construct triangle ABC if hypotenuse c = 7 cm and angle ABC = 30 degrees. / Use Thales' theorem - circle /. Measure and write down the length of legs.
- Triangle ABC
Construct a triangle ABC is is given c = 60mm hc = 40 mm and b = 48 mm analysis procedure steps construction
- Draw a trapezoid
Draw a trapezoid if given a = 7 cm, b = 4 cm, c = 3.5 cm, diagonal AC = 5cm. Solve as a construction task.
- Right triangle
Draw a right triangle ABC if |AB| = 5 cm |BC| = 3 cm, |AC| = 4 cm. Draw Thales circle above the hypotenuse of the triangle ABC.