Question
Is ∆EFG∼∆LMN?
- No, not similar.
- Yes, similar by AA.
- Yes, similar by SSS.
- Yes, similar by SAS.
Hint:
We are given two triangles. The triangles are EFG and LMN. We are also given their two angles. We are asked if they are similar of not. Similar triangles have same shape. Their sizes are different. We will use the properties of the similar triangles to see if the given triangles are similar or not.
The correct answer is: Yes, similar by AA.
The given triangles are EFG and LMN.
We have to show if they are similar or not.
Similar triangles have same shape but different size. Their sides are in proportion. And, the angles of the similar triangles are congruent.
Let’s see their angles.
For the triangle ∆EFG
∠E = 102°
∠F = 30°
For the triangle ∆LMN
∠L = 102°
∠N = 48
We want to see if ∆EFG ~ ∆ LMN
For that the respective angles should be congruent.
Let’s find the value of ∠M
Sum of all angles of triangles should be 180°.
So,
∠L + ∠M + ∠N = 180°
102 + ∠M + 48 = 180
∠M = 30°
Now, if we see
∠E = ∠L
∠F = ∠N
By AA test of similarity, the above triangles are similar.
AA test : If two angles of the triangles are congruent, then the two triangles are said to be similar.
∆EFG ~ ∆ LMN
Yes, they are similar by AA 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
A triangle has sizes measuring 11 cm, 16 cm, and 16 cm. A similar triangle has sides measuring x cm, 24 cm, and 24 cm. Find x?
We should know about different properties of similar triangles. We have to be careful about which sides to choose for the ratio.
A triangle has sizes measuring 11 cm, 16 cm, and 16 cm. A similar triangle has sides measuring x cm, 24 cm, and 24 cm. Find x?
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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.
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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.
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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.
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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.
