The sides of a triangle are 8,15 and 18 the shortest side of a similar triangle is 10 how long are the other sides?
Find the scale factor of similar triangles whose sides are 4,12,20 and 5,15,25
Assume that traingle xyz is similar to triangle rpn with x(ray sign) r and p(ray sign) y. State three proportions that are TRUE
Prove that if one two similar triangles is isosceles, then the other is also isosceles
How to do those please/
so, if these are easy, what's the trouble?
#1. The similar triangle's sides are in the ratio 10:8 = 5/4 as big as the smaller triangle's.
#2. The scaling is obviously 5/4 = 15/12 = 25/20
#3. assuming the vector signs,
x/r = y/p
and two others
#4. Since the sides are all scaled equally, the two equal sides are still equal after scaling.
To find the lengths of the other sides of a similar triangle, we need to determine the scale factor between the two triangles.
1. In the given triangle with sides 8, 15, and 18, divide the length of the corresponding side of the similar triangle (10) by the length of the corresponding side of the original triangle.
Scale factor = 10 / 8 = 1.25
2. Multiply each side length of the original triangle by the scale factor to find the lengths of the sides in the similar triangle.
First side = 8 * 1.25 = 10
Second side = 15 * 1.25 = 18.75
Third side = 18 * 1.25 = 22.5
So, the lengths of the other sides of the similar triangle are 10, 18.75, and 22.5.
To find the scale factor between similar triangles, divide the corresponding side lengths of one triangle by the corresponding side lengths of the other triangle.
1. For the first set of similar triangles with sides 4, 12, 20 and 5, 15, 25:
Scale factor = (4 / 5) = (12 / 15) = (20 / 25) = 0.8
The scale factor for the two triangles is 0.8.
To state three proportions that are true for similar triangles:
Let's assume triangle XYZ is similar to triangle RPN with X̅R and P̅Y. The corresponding side lengths in the two triangles are:
X̅R : X̅P̅ :: Y̅R : Y̅N
X̅P̅ : X̅Y :: P̅N : N̅Y
X̅R : X̅Y :: Y̅R : Y̅N
The first proportion compares the corresponding side lengths X̅R and Y̅R in the two triangles.
The second proportion compares the corresponding side lengths X̅P̅ and P̅N in the two triangles.
The third proportion compares the corresponding side lengths X̅R and Y̅R in the two triangles.
To prove that if one of two similar triangles is isosceles, the other must also be isosceles, we need to use the concept of corresponding angles in similar figures.
Suppose triangle ABC is similar to triangle XYZ. If triangle ABC is isosceles with sides AB = AC, then we need to show that triangle XYZ is also isosceles.
1. We know that corresponding angles in similar triangles are congruent. Denote the corresponding angles as ∠A, ∠B, and ∠C in triangle ABC, and ∠X, ∠Y, and ∠Z in triangle XYZ.
2. Since triangle ABC is isosceles, angles ∠B and ∠C are congruent, so ∠B ≅ ∠C.
3. By the property of corresponding angles, ∠Y ≅ ∠Z in triangle XYZ.
4. Let's assume that sides XY and XZ are not congruent (XY ≠ XZ). If that were the case, it would violate the property of corresponding sides in similar triangles.
5. Since ∠Y ≅ ∠Z and XY ≠ XZ, it would imply that angles ∠X and ∠Y are not congruent, which would contradict the property of corresponding angles.
6. Thus, our assumption that XY ≠ XZ is false, and it follows that sides XY and XZ must be congruent (XY ≅ XZ), making triangle XYZ isosceles.
Therefore, if one of two similar triangles is isosceles, the other must also be isosceles.