Similarity of triangles - practice problemsDirection: Solve each problem carefully and show your solution in each item.
Number of problems found: 139
- 12cm 4365
a = 6cm, b = 8cm, c =? , a '=? , b '= 12cm, c' = 15cm
One of the catheti of the right triangle has a length of 12 cm. At what distance from the center of the hypotenuse is another cathetus?
- Similarity coefficient
The triangles ABC and A'B'C' are similar to the similarity coefficient 2. The sizes of the angles of the triangle ABC are α = 35° and β = 48°. Find the magnitudes of all angles of triangle A'B'C'.
- Triangles 6647
For triangles ABC and A'B'C': alpha = alpha with a line, beta with line = beta. a) are these triangles identical? Why? b) are these triangles similar? Why?
- 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° and beta = 48°. Determine the magnitudes of all angles of triangle A'B'C '.
- Two angles
The triangles ABC and A'B'C 'are similar. In the ABC triangle, the two angles are 25° and 65°. Explain why in the triangle A'B'C 'is the sum of two angles of 90 degrees.
- Similarity of triangles
If triangle ABC ~ to triangle XYZ, AC = 24, AB = 15, BC = 17, and XY = 9, what is the perimeter of triangle XYZ? Round all sides to 1 decimal place.
Are two right triangles similar if the first one has an acute angle 70° and the second one has an acute angle 20°?
- The straight
The straight path rises by 72 cm every 3 m of its length. How many meters will it climb to 350 m?
- The triangles
Two similar triangles, KLM and ABC, are given. Calculate the lengths of the remaining sides of the triangle KLM. If the lengths of the sides are a = 7 b = 5.6 c = 4.9 k = 5
ABC is a triangle wherein a = 4 cm, b = 6 cm, c = 8 cm. Is it similar to the triangle DEF: d = 3 cm, e = 4.5 cm, f = 6 cm? If so, determine the ratio of similarity.
Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and the hypotenuse 8.544.
- See harmonics
Is it true that the size of the central segment of any trapezoid is the harmonic mean size of its bases? Prove it. The central segment crosses the intersection of the diagonals and is parallel to the bases.
- Following 6660
KLM triangle on sides k = 5.4 cm. L = 6 cm, m = 6.6 cm. Construct a triangle K 'L'M 'for which the following holds: ∆KLM ~ ∆K 'L'M' and m '= 9.9cm
- Figure 2
Figure A maps to figure B with a scale factor of 0.75. The length of the line AB segment in figure A is 10. What is its length on the image in figure B?
- Tree shadow
The shadow of the tree is 16 meters long. The shadow of a two-meter-high tourist sign beside standing is 3.2 meters long. What height has a tree (in meters)?
ABCD is a rhombus, ABD is an equilateral triangle, and AC is equal to 4. Find the area of the rhombus.
The road has climbing 1:27. How big is an angle correspond to this climbing?
- Coefficient 4872
Find out if the triangles ABC and A'B'C' are similar, determine the similarity coefficient and write the similarity: a = 40 mm, b = 48 mm, c = 32 mm a´ = 60 mm, b´ = 50 mm, c´ = 40 mm
- Determine 80754
The perimeter of triangle MAK is 216 mm, side a = 81 mm, and side k = 62 mm. Determine the side length of the triangle OSA if the triangle MAK is congruent to the triangle OSA.