Question
Are the triangles similar?
- Yes, by AA
- Not similar
- Yes, by SAS
- Yes, by SSS
Hint:
We are given two triangles. The triangles are ABC and DEF. We are also given the values of 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, by AA
The given triangles are ABC and DEF.
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 ∆ABC
∠C = 90°
∠B = 35°
For the triangle ∆DEF
∠D = 55°
∠F = 90°
We want to see if ∆ABC ~ ∆DEF
For that the respective angles should be congruent.
Let’s find the value of ∠E
Sum of all angles of triangles should be 180°.
So,
∠F + ∠D + ∠E = 180°
90 + ∠D + 55 = 180
∠D = 35°
Now, if we see
∠B = ∠D
∠C = ∠F
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.
∆ABC ~ ∆DEF
Yes, they are similar by AA test.
For such questions, we should know the properties of similar triangles. We should also know the tests required to prove if triangles are similar or not.
Related Questions to study
Find the person height.
For such questions, we should know the properties of both right angled triangles and similar triangles. We should know about different tests to see if the triangles are similar or not.
Find the person height.
For such questions, we should know the properties of both right angled triangles and similar triangles. We should know about different tests to see if the triangles are similar or not.
A picture of a school’s mascot is 18 in. wide and 24 in. long. It is enlarged proportionally to banner size. If the width is enlarged to 54 in., The length of the banner is?
For such questions, we should know the properties of the similar objects.
A picture of a school’s mascot is 18 in. wide and 24 in. long. It is enlarged proportionally to banner size. If the width is enlarged to 54 in., The length of the banner is?
For such questions, we should know the properties of the similar objects.
ByTo find the height of a very tall pine tree, you place a mirror on the ground and stand where you can see the top of the pine tree. Find the tree tall .
For such questions, we should know about the properties of similar triangle. We should also know about different tests required to prove the similarity.
ByTo find the height of a very tall pine tree, you place a mirror on the ground and stand where you can see the top of the pine tree. Find the tree tall .
For such questions, we should know about the properties of similar triangle. We should also know about different tests required to prove the similarity.
Is ∆EFG∼∆LMN?
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.
Is ∆EFG∼∆LMN?
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 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?
We should know about different properties of similar triangles. We have to be careful about which sides to choose for the ratio.
Two objects that are the same shape but not the same size are _______.
The objects which are identical are called as congruent objects.
Two objects that are the same shape but not the same size are _______.
The objects which are identical are called as congruent objects.
Are the two triangles are similar?
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.
Are the two triangles are similar?
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.
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.
