Question

Please help me. its attached

Answer 1

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 = $\sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

Coordinates of A = (1, 4) and B = (2, 2).

Now plug in these values in to the distance formula.

AB = $\sqrt{(2 -1)^2 + (2 - 4)^2}$

AB = $\sqrt{(1)^1 + (-2)^2}$

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 = $\sqrt{(5 - 1)^2 +(2 - 4)^2}$

AC = $\sqrt{(4)^2 + (-2)^2}$

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.