# Geometry - problems

- Reverse Pythagorean theorem

Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 73 m, 66 m, 51 m ? Δ DEF: 63 cm, 105 cm, 84 cm ? Δ GHI: 50 dm, 48 dm, 14 dm ? Δ JKL: 31 m, 45 m, 40 m ? Δ MNO: 28 m, 53 m, 45 m ? - Crossroads

The rectangular crossroads comes passenger car and an ambulance, the ambulance left. Passenger car is at 45 km/h and ambulance 58 km/h. Calculate such a relative speed of the ambulance moves to the car. - Geodesist

Triangle shaped field (triangle ABC) has side AB = 51 m. path XY is parallel to the side AB which divided triangle ABC into two parts with same area. What will be the length of the path XY? Help please geodesist ... - Perpendicular

Determine the slope of the line perpendicular to the line p: y = 9x +7. - Vector

Determine coordinates of the vector u=CD if C[13;-8], D[-19,-13]. - 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 - Triangle IRT

In isosceles right triangle ABC with right angle at vertex C is coordinates: A (-1, 2); C (-5, -2) Calculate the length of segment AB. - 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. - Chors centers

The circle with a diameter 17 cm, upper chord /CD/ = 10.2 cm and bottom chord /EF/ = 7.5 cm. The midpoints of the chords H, G is that /EH/ = 1/2 /EF/ and /CG/ = 1/2 /CD/. Determine the distance between the G and H, if CD II EF (parallel). - Euclid theorems

Calculate the sides of a right triangle if leg a = 6 cm and a section of the hypotenuse, which is located adjacent the second leg b is 5cm. - Medians and sides

Triangle ABC in the plane Oxy; are the coordinates of the points: A = 2.7 B = -4.3 C-6-1 Try calculate lengths of all medians and all sides. - Tree shadow

Tree perpendicular to the horizontal surface has a shadow 8.32 meters long. At the same time meter rod perpendicular to the horizontal surface has shadow 64 cm long. How tall is tree? - Diagonals

Draw a square ABCD whose diagonals have a length of 6 cm - Hexagon

There is regular hexagon ABCDEF. If area of the triangle ABC is 19, what is area of the hexagon ABCDEF? I do not know how to solve it simply.... - Slope

What is the slope of a line with an inclination 1.06 rad? - Height

Is right that in any right triangle height is less or equal half of the hypotenuse? - Pentagon

Within a regular pentagon ABCDE point P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch. - Vector sum

The magnitude of the vector u is 8 and the magnitude of the vector v is 11. Angle between vectors is 65°. What is the magnitude of the vector u + v? - Rectangular triangles

The lengths of corresponding sides of two rectangular triangles are in the ratio 2:5. At what ratio are medians relevant to hypotenuse these right triangles? At what ratio are the contents of these triangles? Smaller rectangular triangle has legs 6 and 8 c - Trapezoid IV

In a trapezoid ABCD (AB||CD) is |AB| = 15cm |CD| = 7 cm, |AC| = 12 cm, AC is perpendicular to BC. What area has a trapezoid ABCD?

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