Answer
5. ΔABC ≅ ΔDEF is true.
6. ΔABC ≅ ΔGHI is not true.
Step by step explanation
5. Find the lengths of the triangle ABC.
BC = 3
Use the distance formula to find the length of AB and AC
Distance formula = [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]
Coordinates of A = (1, 4) and B = (2, 2).
Now plug in these values in to the distance formula.
AB = [tex]\sqrt{(2 -1)^2 + (2 - 4)^2} \\[/tex]
AB = [tex]\sqrt{(1)^1 + (-2)^2}[/tex]
AB = √1 + 4
AB = √5
Now let's find the length of AC.
A = (1, 4), C = (5, 2)
Use the distance formula and the length of AC.
AC = [tex]\sqrt{(5 - 1)^2 +(2 - 4)^2}[/tex]
AC = [tex]\sqrt{(4)^2 + (-2)^2}[/tex]
AC = √(16 + 4)
AC = √20
Now let's find the length of GI
G = (6, 6) and I = (8, 1)
Use the distance formula.
GI = √(2)^2 + (-5)^2
GI = √(4 + 25)
GI = √29.
The length of EF = 3, DE = √5, EF = √20
Now let's compare the two triangles ABC and DEF.
The sides of the triangle ABC is equal to the sides of the triangle DEF
By SSS property, ΔABC ≅ ΔDEF.
6) The side length of GI = √29 which is not equal to the side length of AC = √20.
Therefore, the ΔABC ≅ ΔGHI is not true.
Hope this will help you.
Thank you.
