Euclid's theorems - practice problems - page 2 of 4
It is usually teach in high school. The Pythagorean theorem can be easily proved using Euclid's theorems.Direction: Solve each problem carefully and show your solution in each item.
Number of problems found: 61
- Perpendicular projections
In a right-angled triangle, the perpendicular projections of the legs on the hypotenuse have lengths of 3.1 cm and 6.3 cm. Calculate the perimeter of this triangle. Round the result to the nearest hundredth of a centimeter. - Hypotenuse and height
In a right triangle is length of the hypotenuse c = 195 cm and height hc = 70 cm. Determine the length of both triangle legs. - Area of RT
Calculate the area of a right triangle in which the hypotenuse has length 14 and one of the segments that the altitude creates on the hypotenuse has length 5. - Euclid3
Calculate the height and sides of the right triangle if one leg is a = 100 km and the section of hypotenuse adjacent to the second leg cb = 14 km. - Quadrilateral circle radius
Given is a quadrilateral ABCD inscribed in a circle, with the diagonal AC being the circle's diameter. The distance between point B and the diameter is 15 cm, and between point D and the diameter is 18 cm. Calculate the radius of the circle and the perime - RT sides
Find the sides of a rectangular triangle if legs a + b = 17 cm and the radius of the written circle ρ = 2 cm. - Right Δ
A right triangle has one leg 54 cm long and a hypotenuse 90 cm long. Calculate the altitude from the right angle to the hypotenuse. - Tangents
From point R, two tangents are drawn to a circle with a radius of 41 cm. The distance between the two points of tangency is 16 cm. Calculate the distance from point R to the centre of the circle. - Triangle height ratio
In the right-angled triangle ABC (AB is the hypotenuse), a : b = 24 : 7, and the height to the side c = 12.6 cm applies. Calculate the lengths of the sides of triangle ABC. - Hypotenuse height segments
We know the height of the hypotenuse h = 4 cm and the hypotenuse c = 19 cm in a right triangle. How to calculate the segments of legs - sections on the hypotenuse c1, c2 - Rhombus and inscribed circle
It is given a rhombus with side a = 6 cm and the inscribed circle r = 2 cm radius. Calculate the length of its two diagonals. - Rectangle
In rectangle ABCD with sides |AB|=19, |AD|=19, a perpendicular is drawn from point A to diagonal BD, meeting it at point P. Determine the ratio r = (|PB|)/(|DP|). - Right triangle - ratio
The lengths of the legs of the right triangle ABC are in ratio b = 2:3. The hypotenuse is 10 cm long. Calculate the lengths of the legs of that triangle. - Medians in right triangle
It is given a right triangle, and angle C is 90 degrees. I know it medians t1 = 8 cm and median t2 = 12 cm. How to calculate the length of the sides? - Rhombus
A rhombus has a side length of a = 20 cm. The points where the inscribed circle touches the sides divide each side into segments of length a₁ = 13 cm and a₂ = 7 cm. Calculate the radius r of the inscribed circle and the lengths of the diagonals of the rho - Right triangle area
In a right-angled triangle ABC, the height of side c has a length of 6 cm. The letter D indicates the heel of the height. Line segment AD is 8 cm long. Calculate the area of triangle ABC. ( example on Monitor 9 ) - Right isosceles triangle
The right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse, dividing it into two equal segments. One segment is 5 cm long. What is the area of the triangle? - Right 24 The right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse, dividing it into two unequal segments. One segment is 5 cm long. What is the area of the triangle? Thank you.
- Triangle KLM
In the rectangular triangle KLM, where |KL|=m is the hypotenuse (sketch it!). Find the length of the leg k and the height of triangle h if the hypotenuse's segments are known MK = 5 cm and ml = 15 cm. - Segments on the hypotenuse
A right triangle ABC has a hypotenuse c = 26 cm. The altitude from C to the hypotenuse is h_c = 12 cm. What are the lengths of the two segments of the hypotenuse? What are the lengths of sides a and b? What are the angles at vertices A and B?
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