Name the congruent triangles and justify the reason for congruence.

δabc ≅ δfde by hl
δabc ≅ δedf by asa
δabc ≅ δfed by hl
δabc ≅ δfed by asa

Step-by-step explanation:

If we observe each triangle in the image, we will notice that they have two congruent angles(, and ), also .

Based on this facts, we can use the Angle-Side-Angle Postulate to say that , in that order, because , and  ;  

The justified reason is : ΔABC ≅ ΔEDF by SSS

Step-by-step explanation:

Given : ΔABC and ΔEDF

∠C = 135° ,∠B = 30°

∠D = 30° , ∠F = 135°

To show : ΔABC ≅ ΔEDF are by which congruence rule:

Proof:

In ΔABC:

AB = A(0,0), B(2,4)

Distance formula:

BC = B(2,4) ,(0,2)

AC = A(0,0), C(0,2)

In ΔEDF:

DE= D(2,0), E(4,4)

EF= E(4,4) ,F(4,2)

DF= D(2,0), F(4,2)

In ΔABC and  ΔEDF

AB = ED =

AC = EF =

BC = DF =

ΔABC ≅ ΔEDF by SSS

really really sorry if i'm

-12 -5(x + 4) = 3x

-12 - 5x - 20 = 3x

-12 - 20 - 5x = 3x

-32 - 5x = 3x

    + 5x   + 5x

-32 = 8x

8         8

- 4= x

there are infinitely many solutions.