Similarity of triangles - practice problems - page 2 of 7
Number of problems found: 125
- MO Z7–I–6 2021
In triangle ABC, point D lies on the AC side and point E on the BC side. The sizes of the angles ABD, BAE, CAE, and CBD are 30°, 60°, 20°, and 30°, respectively. Find the size of the AED angle. - Circumference 42471
The lengths of the sides of the triangle ABC are in the ratio 4: 2: 5. Calculate the size of the longest side of a similar KLM triangle, whose circumference is 66 cm. - Right-angled 40961
A right-angled triangle ABC has sides a = 5 cm, b = 8 cm. The similar triangle A'B'C' is 2.5 times smaller. Calculate what percentage of the area of triangle ABC is the area of triangle A'B'C'. - A cliff
A line from the top of a cliff to the ground passes just over the top of a pole 5 ft high and meets the ground at a point 8 ft from the base of the pole. If the point is 93 ft from the base of the cliff, how high is the cliff? - 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 at the same time. - Triangle-shaped 30011
Determine the map's scale if the 1.6 km, 2.4 km, and 2.7 km triangle-shaped forests are drawn on the map as a triangle with sides of 32 mm, 48 mm, and 54 mm. - Vertical 29801 The shadow of the building is 16 m long, and the shadow of the vertical meter rod is 0.8 m long at the same time. What is the height of the building?
- The straight
The straight path rises by 72 cm every 3 m of its length. How many meters will it climb to 350 m? - Poplar shadow The nine-meter poplar casts a shadow 16.2 m long. How long does a shadow cast by Peter at the same time, if it is 1.4 m high?
- Distance of points
A regular quadrilateral pyramid ABCDV is given, in which edge AB = a = 4 cm and height v = 8 cm. Let S be the center of the CV. Find the distance of points A and S. - Inclined plane
The body stays on an inclined plane and exerts a compressive force of 70N on it. Find the angle between the inclined plane and the horizontal if a gravitational force of 100N acts on the body. - Chimney and tree Calculate the height of the factory chimney, which casts a shadow 6.5 m long in the afternoon. At the same time, a 6 m high tree standing near it casts a shadow 25 dm long.
- Similar triangles
Triangle A'B'C 'is similar to triangle ABC, whose sides are 5 cm, 8 cm, and 7 cm long. What is the length of the sides of the triangle A'B'C' if its circumference is 80 cm? - The triangles
The triangles ABC and A'B'C 'are similar with a similarity coefficient of 2. The angles of the triangle ABC are alpha = 35°, beta = 48°. Determine the magnitudes of all angles of triangle A'B'C '. - Similar triangles
The triangles ABC and XYZ are similar. Find the missing lengths of the sides of the triangles. a) a = 5 cm b = 8 cm x = 7.5 cm z = 9 cm b) a = 9 cm c = 12 cm y = 10 cm z = 8 cm c) b = 4 cm c = 8 cm x = 4.5 cm z = 6 cm - Triangle 28611 The land has the shape of a triangle with sides of 300m, 200m, and 245m. Draw it on a scale of 1: 5 000.
- Equilateral cone
We pour so much water into a container that has the shape of an equilateral cone, the base of which has a radius r = 6 cm, that one-third of the volume of the cone is filled. How high will the water reach if we turn the cone upside down? - Similar triangles
In the triangle DEF is DE = 21cm, EF = 14.7cm, DF = 28cm. The triangle D´E´F´ is similar to the triangle DEF. Calculate the lengths of the sides of the triangle D´E´F´ if the similarity coefficient is one-seventh. - Similarity coefficient
In the triangle TMA the length of the sides is t = 5cm, m = 3.5cm, a = 6.2cm. Another similar triangle has side lengths of 6.65 cm, 11.78 cm, 9.5 cm. Determine the similarity coefficient of these triangles and assign similar sides to each other. - Meneal's 26771 Show (using Meneal's theorem) that the center of gravity divides the line in a 1: 2 ratio.
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