Question

Can anyone help me with this? im confused

Answer 1

1,2,3 and 6 are similar triangles by AA similarity

Explanation:

1) ∠DEC ≅ ∠FEG {Vertically opposite angles}

DC // GF

∠ECD ≅ ∠EGF {Alternate interior angles}

∠EDC ≅ ∠EFG {Alternate interior angles}

ΔDEC & ΔFEG are similar triangles by AA similarity

2)MN // QP

∠LQP ≅ ∠QMN {Corresponding angles }

∠LPQ ≅ ∠PNM {Corresponding angles}

ΔLQP & ΔLMN are similar triangles by AA similarity

3) In ΔSYE ,

∠S = 180 - 90 - 39

∠S = 51°

In ΔCHW,

∠H = 180 - 51 - 90

∠H = 39

ΔSYE and ΔCHW

∠S ≅ ∠W = 51°

∠Y ≅ ∠C = 90°

∠E ≅∠H = 39°

ΔSYE & ΔWCH are similar triangles by AA similarity

6) ∠P ≅ ∠Z {Given}

∠PXQ ≅∠ZXY {Vertically opposite angles}

ΔPXQ & ΔZXY are similar triangles by AA similarity