Question
Are the two triangles are similar?
- Yes, they are similar by SAS.
- No, they're not similar.
- Yes, they're similar by AA
- Yes, they are similar by SSS.
Hint:
We are given the height of a pole and length of the shadow formed by it. We are also given the length of shadow of the building. It is stated that the shadows are casts at the same time. As the shadows are at the same time, their angles will be same. If we joined the ends of the building and the pole with their shadows, triangles are formed.
The correct answer is: Yes, they are similar by SSS.
The given triangles are ABC and HGF.
We have to show if they are similar or not.
Similar triangles have following properties.
1) They have same shape.
2) The angles are same.
3) They have different sizes.
4) Their sides are in proportion. The ratio of the sides are equal.
Let’s take the ratio of the sides of the above triangles.
We can see that the ratio of the sides is equal.
SSS test: If the sides of the triangles are in proportion, then the triangles are similar.
Therefore, the above triangles are similar by SSS test.
We should know about different properties of similar triangles. We have to be careful about which sides to choose for the ratio. We should also know about different similarity tests.
Related Questions to study
You are making a guitar pick that resembles an equilateral triangle with side lengths of 32 millimeters. The approximate height of the pick is?
For such questions, the properties of right-angled triangles are important. We should know about the trigonometric ratios. It includes sine, cosine, tangent etc.
You are making a guitar pick that resembles an equilateral triangle with side lengths of 32 millimeters. The approximate height of the pick is?
For such questions, the properties of right-angled triangles are important. We should know about the trigonometric ratios. It includes sine, cosine, tangent etc.
Find the value of y, if you know the value of x=16
We should know the properties of a right-angled triangle. Pythagoras theorem is very important while solving the questions of a right-angled triangle.
Find the value of y, if you know the value of x=16
We should know the properties of a right-angled triangle. Pythagoras theorem is very important while solving the questions of a right-angled triangle.
A power pole 10 m tall casts a shadow 8 meters long, at the same time that a building nearby casts a shadow 14 m long. Find the building tall.
We should know about different properties of similar triangles. We have to be careful about which sides to choose for the ratio. We should also know about different similarity tests.
A power pole 10 m tall casts a shadow 8 meters long, at the same time that a building nearby casts a shadow 14 m long. Find the building tall.
We should know about different properties of similar triangles. We have to be careful about which sides to choose for the ratio. We should also know about different similarity tests.
Find the length of the altitude of triangle PQR.
To solve such questions, we should know the properties of right-angled triangles and similar triangles. Similar triangles have different sizes, but are of same shape. Their sides are in different proportion, but their angles are same. As a shortcut, we can just remember the last step of the above expression.
Find the length of the altitude of triangle PQR.
To solve such questions, we should know the properties of right-angled triangles and similar triangles. Similar triangles have different sizes, but are of same shape. Their sides are in different proportion, but their angles are same. As a shortcut, we can just remember the last step of the above expression.
Find the value of y.
For such questions, we should know the properties of right-angled triangle. We should know the trignometric ratios. The values of different sines and cosines should be known.
Find the value of y.
For such questions, we should know the properties of right-angled triangle. We should know the trignometric ratios. The values of different sines and cosines should be known.
A square has side length 95. The length of the diagonal of the square is? Express your answer in simplest radical form.
For such questions, we should know the properties of the right-angled triangle. The other method to solve it will be 45°-45°-90° theorem. Due to diagonal, the triangle which is formed has the sides in proportion 1:1:√2. Therefore, the value of hypotenuse is given by √2 multiplied by the value of the side.
A square has side length 95. The length of the diagonal of the square is? Express your answer in simplest radical form.
For such questions, we should know the properties of the right-angled triangle. The other method to solve it will be 45°-45°-90° theorem. Due to diagonal, the triangle which is formed has the sides in proportion 1:1:√2. Therefore, the value of hypotenuse is given by √2 multiplied by the value of the side.
