APPLYING THE SCALE FACTOR OF SIMILAR TRIANGLES TO THE PERIMETER
The scale factor of two similar triangles (or any geometric shape, for that matter) is the ratio between two corresponding sides.
In today's lesson, we will show that this same scale factor also applies to the ratio of the two triangles' perimeter. This is fairly easy to show, so today's lesson will be short.
PROBLEM
Two triangles, ΔABC and ΔADE are similar, ΔABC∼ ΔADE. The scale factor, AB/AD is 6/5. Find the ratio of the perimeters of the two triangles.
Similar triangles in geometry
STRATEGY
We will use the definition of the scale factor to define one set of sides in terms of the other set of sides, Then, apply the definition of the perimeter. and write out the perimeter of both triangles using one set of sides.
SOLUTION
(1) ΔABC∼ ΔADE //Given
(2) AB/AD = 6/5 //Given
(3) BC/DE = 6/5 //(1), (2), scale factor is the same for all sides in similar triangles.
(4) AC/AE = 6/5 //(1), (2), scale factor is the same for all sides in similar triangles.
(5) AB = 6/5*AD // rearrange (2)
(6) BC = 6/5*DE // rearrange (3)
(7) AC = 6/5*AE // rearrange (4)
(8) PABC=AB+BC+AC //definition of perimeter
(9) PADE=AD+DE+AE //definition of perimeter
(10)PABC=6/5AD+6/5DE+ 6/5*AE //(8), (5), (6) , (7), Transitive property of equality
(11)PABC=6/5*(AD+DE+AE) //(10), Distributive property of multiplication
(12) PABC=6/5*PADE //(11), (9), Transitive property of equality
(13) PABC/PADE=6/5
And so we have easily shown that the scale factor of similar triangles is the same for the perimeters.
ABC angle is an angle,not a triangle!
Classification of Triangles According to anglesIf one angle of a triangle is a right angle (90°), then it is called a Right triangle. Note that the other two angles are acute.If all the angles of a triangle are acute (less than 90°), then it is called an acute angled triangle.If one angle of a triangle is obtuse (greater than 90°), then it is called an obtuse triangle. Note that the other two angles are acute.According to sides:If any two sides of a triangle are equal, then it is called an Isosceles Triangle. In ABC, AB = AC ABC is isosceles.If all the three sides of a triangle are equal, then it is an Equilateral Triangle. In ABC, AB = BC = CA ABC is equilateral.If no two sides of a triangle are equal, then it is called a Scalene Triangle. In ABC, AB BC CA. ABC is scalene.
90
(c2) / (2 cot A + cot B) = Area of Triangle ABC
If triangles ABC and DCE have the same angles then yes otherwise no.
Find the coordinates of the vertices of triangle a'b'c' after triangle ABC is dilated using the given scale factor then graph triangle ABC and its dilation A (1,1) B(1,3) C(3,1) scale factor 3
the sides of ABC are congruent to the sides of A'B'C'
0.5
If you mean: 8 12 16 and 10 15 20 then it is 4 to 5
Answer: Since you are looking for the scale factor of ABC to DEF the answer is 8 because DEF is 8 times larger than ABC.
6 apex
4,8,12
the answer would be 10 0n apex
ABC angle is an angle,not a triangle!
It is isosceles.
It is isosceles.
They are 17 times AB, BC and Ca, respectively.