The similarity ratio is the constant difference between the corresponding sides of the two shapes.
That is, if the similarity ratio is , we know that each side of the large triangle is times larger than that of the small triangle.
The similarity ratio is the constant difference between the corresponding sides of the two shapes.
That is, if the similarity ratio is , we know that each side of the large triangle is times larger than that of the small triangle.
The calculation of the similarity ratio is divided into several steps that must be performed:
The result obtained is actually the similarity ratio.
\( ΔACB∼ΔBED \)
Choose the correct answer.
What is the ratio between the sides of the triangles ΔABC and ΔMNA?
Is the similarity ratio between the three triangles equal to one?
BC is parallel to DE.
Fill in the gap:
\( \frac{AD}{}=\frac{AE}{AC} \)
Triangle DFE is similar to triangle ABC.
Calculate the length of FE.
Choose the correct answer.
First, let's look at angles C and E, which are equal to 30 degrees.
Angle C is opposite side AB and angle E is opposite side BD.
Now let's look at angle B, which is equal to 90 degrees in both triangles.
In triangle ABC the opposite side is AC and in triangle EBD the opposite side is ED.
Let's look at angles A and D, which are equal to 60 degrees.
Angle A is the opposite side of CB, angle D is the opposite side of EB
Therefore, from this it can be deduced that:
And also:
Answers a + b are correct.
What is the ratio between the sides of the triangles ΔABC and ΔMNA?
From the data in the drawing, it seems that angle M is equal to angle B
Also, angle A is an angle shared by both triangles ABC and AMN
That is, triangles ABC and AMN are similar respectively according to the angle-angle theorem.
According to the letters, the sides that are equal to each other are:
Now we can calculate the ratio between the sides of the given triangles:
Is the similarity ratio between the three triangles equal to one?
To answer the question, we first need to understand what "similarity ratio" means.
In similar triangles, the ratio between the sides is constant.
In the statement, we do not have data on any of the sides.
However, a similarity ratio of 1 means that the sides are exactly the same size.
That is, the triangles are not only similar but also congruent.
In the drawing, you can clearly see that the triangles are of different sizes and, therefore, clearly the similarity ratio between them is not 1.
No
BC is parallel to DE.
Fill in the gap:
Since we are given that line BC is parallel to DE
Angle E equals angle C and angle D equals angle B - corresponding angles between parallel lines are equal.
Now let's observe that angle D is opposite to side AE and angle B is opposite to side AC, meaning:
Now let's observe that angle E is opposite to side AD and angle C is opposite to side AB, meaning:
AB
Triangle DFE is similar to triangle ABC.
Calculate the length of FE.
Let's look at the order of letters of the triangles that match each other and see the ratio of the sides.
We will write accordingly:
Triangle ABC is similar to triangle DFE
The order of similarity ratio will be:
Now let's insert the existing data we have in the diagram:
Let's reduce y and we get:
What is the ratio of similarity between the triangles shown in the diagram below?
According to which theorem are the triangles similar?
What is their ratio of similarity?
In the image there are a pair of similar triangles and a triangle that is not similar to the others.
Determine which are similar and calculate their similarity ratio.
The triangles above are similar.
Calculate the perimeter of the larger triangle.
The similarity ratio between two similar triangles is 7, so that the area ratio is \( _{——} \)
What is the ratio of similarity between the triangles shown in the diagram below?
From the drawing it appears that angle E equals angle A
Since angle D equals 90 degrees, its adjacent angle also equals 90 degrees.
In other words, angle D1 equals angle D2 and both equal 90 degrees.
Since we have two pairs of equal angles, the triangles are similar.
Also angle B equals angle C
Now let's write the similar triangles according to their corresponding angle letters:
Let's write the ratio of sides according to the corresponding letters of the similar triangles:
According to which theorem are the triangles similar?
What is their ratio of similarity?
Using the given data, the side ratios can be written as follows:
We can therefore deduce that the ratio is compatible with the S.S.S theorem (Side-Side-Side):
S.S.S.,
In the image there are a pair of similar triangles and a triangle that is not similar to the others.
Determine which are similar and calculate their similarity ratio.
Triangle a and triangle b are similar according to the S.S.S (side side side) theorem
And the relationship between the sides is identical:
That is, the ratio between them is 1:3.
and , similarity ratio of
The triangles above are similar.
Calculate the perimeter of the larger triangle.
We calculate the perimeter of the smaller triangle (top):
Due to their similarity, the ratio between the sides of the triangles is equal to the ratio between the perimeters of the triangles.
We will identify the perimeter of the large triangle using :
36
The similarity ratio between two similar triangles is 7, so that the area ratio is
We square it. 7 squared is equal to 49.
49
BC is parallel to DE.
Calculate AE.
The triangle above are similar.
What is the perimeter of the blue triangle?
Here are two similar triangles. The ratio of the lengths of the sides of the triangle is 3:4, what is the ratio of the areas of the triangles?
If the ratio of the areas of similar triangles is 1:16, and the length of the side of the larger triangle is 42 cm, what is the length of the corresponding side in the smaller triangle?
The triangle ABC is similar to the triangle DEF.
The ratio between the lengths of their sides is 9:8.
What is the ratio between the areas of the triangles?
BC is parallel to DE.
Calculate AE.
Let's prove that triangles ADE and ABC are similar using:
Since DE is parallel to BC, angles ADE and ABC are equal (according to the law - between parallel lines, corresponding angles are equal)
Angle DAE and angle BAC are equal since it's the same angle
After we proved that the triangles are similar, let's write the given data from the drawing according to the following similarity ratio:
We know that -
Let's reduce the fractions:
This statement is incorrect, meaning the data in the drawing contradicts the fact that the triangles are similar. Therefore, the drawing is impossible.
Impossible as the shape in the figure cannot exist.
The triangle above are similar.
What is the perimeter of the blue triangle?
The perimeter of the left triangle: 13+12+5=25+5=30
Therefore, the perimeter of the right triangle divided by 30 is equal to 5.2 divided by 13:
12
Here are two similar triangles. The ratio of the lengths of the sides of the triangle is 3:4, what is the ratio of the areas of the triangles?
Let's call the small triangle A and the large triangle B, let's write the ratio:
Square it:
Therefore, the ratio is 9:16
9:16
If the ratio of the areas of similar triangles is 1:16, and the length of the side of the larger triangle is 42 cm, what is the length of the corresponding side in the smaller triangle?
The ratio of similarity is 1:4
The length of the corresponding side in the small triangle is:
10.5
The triangle ABC is similar to the triangle DEF.
The ratio between the lengths of their sides is 9:8.
What is the ratio between the areas of the triangles?
We multiply the ratio by 2
Raised to the power of 2:
81:64