Similarity of triangles - practice problems - page 5 of 8
Number of problems found: 147
- Similarity of two triangles
The KLM triangle has a side length of k = 6.3cm, l = 8.1cm, m = 11.1cm. The triangle XYZ has a side length of x = 8.4cm, y = 10.8cm, z = 14.8cm. Are triangle KLM and XYZ similar? (write 0. If not, if yes, find and write the coefficient of a similarity) - Trapezium diagonals
It is given trapezium ABCD with bases | AB | = 12 cm, |CD| = 8 cm. Point S is the intersection of the diagonals for which |AS| is 6 cm long. Calculate the length of the full diagonal AC. - Thales
Thales is 1 m from the hole. The eyes are 150 cm above the ground and look into the hole with a diameter of 120 cm, as shown. Calculate the depth of the hole. - Shadow and light
Nine meters height poplar tree has a shadow 16.2 meters long. How long does shadow have at the same time as Joe if he is 1,4m tall? - Isosceles 7661
The area of the isosceles triangle is 8 cm2, and its arm's length is 4 cm. Calculate the sizes of its interior angles. - Mast angles and height
Calculate the height of the mast, whose foot can be seen at a depth angle of 11° and the top at a height angle of 28°. The mast is observed from a position 10 m above the level of the base of the mast. - Vertical rod
The vertical one-meter-long rod casts a shadow 150 cm long. Calculate the height of a column whose shadow is 36 m long simultaneously. - Display case
Place a glass shelf at the height of 1m from the bottom of the display case in the cabinet. How long platter will we place at this height? The display case is a rectangular triangle with 2 m and 2.5 m legs. - Isosceles trapezoid
In an isosceles trapezoid KLMN, the intersection of the diagonals is marked by the letter S. Calculate the area of the trapezoid if /KS/: /SM/ = 2:1 and a triangle KSN is 14 cm². - Triangle KLB
It is given equilateral triangle ABC. From point L, the midpoint of the side BC of the triangle, it is drawn perpendicular to the side AB. The intersection of the perpendicular and the side AB is point K. How many percents of the area of the triangle ABC - Area and two angles
Calculate the size of all sides and internal angles of a triangle ABC if it is given by area S = 501.9; and two interior angles α = 15°28' and β = 45°. - Geodesist
Triangle-shaped field (triangle ABC) has a side AB = 129 m. path XY is parallel to the side AB, which divides triangle ABC into two parts with the same area. What will be the length of path XY? Help, please, geodesist. - Triangle 81484
Choose a triangle that is similar to the given triangle. - ∆ TFC= t= 8 cm, f= 9 cm, c= 7 cm. : ∆ PKU= p= 45 cm, k= 35 cm, u= 40 cm. ∆ UPK= u= 40 cm, p= 45 cm, k= 35 cm. ∆ PUK= p= 45 cm, u= 40 cm, k= 35 cm. ∆ KPU= k= 35 cm, p= 45 cm, u= 40 cm. ∆ KUP= k= 35 - Similarity 80742
Calculate the perimeter of triangle ABC if you know that it is similar to triangle EFG in which e=144 mm, f=164 mm, g=92 mm, and the similarity ratio is 4. Express the result in cm. - Circumference 64104
The ABC triangle has a circumference of 11 cm. Triangle A'B'C ', similar to triangle ABC, has side lengths of 6 cm, 120 mm, and 1.5 dm larger than triangle ABC. Calculate the area of the triangle A'B'C '. - Identical 8831
In the triangle ABC, the point P lies closer to point A in the third of the line AB, the point R is closer to the point P in the third of the line P, and the point Q lies on the line BC so that the angles P CB and RQB are identical. Determine the ratio of - A cone 4
A cone with a radius of 10 cm is divided into two parts by drawing a plane through the midpoint of its axis parallel to its base. Compare the volumes of the two parts. - Area of iso-trap
Find the area of an isosceles trapezoid if the lengths of its bases are 16 cm and 30 cm, and the diagonals are perpendicular to each other. - Climb
The road sign which informs the climb is 8.7%—the car drive 5 km along this road. What is the height difference that the car went? - Triangular 29781
A triangular building plot is drawn on a 1:5,000 scale plan as a triangle with sides of lengths 32.5 mm, 23.5 mm, and 36 mm. Determine how many m of mesh are needed to fence the entire plot.
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