Explain why the triangles are similar. Then find the missing length, x. 5 m 8 m 4 m 10 m X 6 m Choose the reason that the triangles are similar A. Both triangles contain right angles and a corresponding angle of equal measure. Thus, two angles of the large triangle are equal in measure to two angles of the small triangle B. All right triangles are similar. C. Both triangles are right and scalene. OD The Pythagorean theorem states that a + b = c2. Thus, the corresponding sides are proportional. Find the missing length 2 X= m

A. Both triangles contain right angles and a corresponding angle of equal measure. Thus, two angles of the large triangle are equal in measure to two angles of the small triangle

x = 3 m

Step-by-step explanation:

The figure given shows two right angles triangles having corresponding angles that are congruent and of the same measure.

If we find the ratios of their given corresponding side lengths, their ratios would be the same.

Thus: ratio of the side of the smaller ∆ to the larger ∆ = 4:8 = 5:10 = 4/8 = 5/10 = ½

½ is the scale factor. Therefore, both triangles are similar.

To find x, multiply the corresponding side length of the other triangle by the scale factor.

x corresponds to side length that is 6 m in the other triangle.

Therefore,

x = 6*½ = 3 m

keshavgandhi04 keshavgandhi04 · Answer 2 · 2021-12-17T10:54:02+01:00

The value of 'x' in the smaller triangle is 2 and both the triangles are similar because triangles contain right angles and a corresponding angle of equal measure. Therefore, two angles of the large triangle are equal in measure to two angles of the small triangle.

Given :

Two triangles are given in the figure.

The Pythagorean theorem can be used in order to determine the value of 'x' in the smaller triangle.

[tex]5^2=4^2+x^2[/tex]

[tex]x^2= 25-16[/tex]

x = 3

According to the given figure of the triangles, both triangles contain right angles and a corresponding angle of equal measure. Therefore, two angles of the large triangle are equal in measure to two angles of the small triangle. Hence both the triangles are similar.

Therefore, the correct option is A).

For more information, refer to the link given below:

https://brainly.com/question/10652623