Answer:
2) ΔDCB ~ ΔDST by SAS similarity.
3) ΔHGF and ΔQRS are not similar triangles.
4) ΔTUV ~ ΔTGH by AA similarity.
5) ΔWVU ~ ΔWFG by AA similarity.
6) ΔUVV and ΔUQR are not similar triangles.
Step-by-step explanation:
Rules of similar triangles:
- AA similarity: Two pairs of corresponding angles are equal.
- SSS similarity: Three pairs of corresponding sides are proportional.
- SAS similarity: Two pairs of corresponding sides are proportional and the corresponding angles between them are equal.
2) In ΔDCB & ΔDST,
∠SDT = ∠CDB {Vertically opposite angles}
[tex]\sf \dfrac{SD}{DC} =\dfrac{24}{40} = \dfrac{3}{5}\\\\\\\dfrac{TD}{DB}=\dfrac{42}{70}=\dfrac{3}{5}\\\\\\\dfrac{SD}{DC}=\dfrac{TD}{DB}=\dfrac{3}{5}\\\\[/tex]
∠SDT = ∠CDB {Vertically opposite angles}
Answer: ΔDCB ~ ΔDST by SAS similarity.
3) ΔHGF and ΔQRS are not similar triangles.
4) In ΔTUV and ΔTGH
∠VTU = ∠HTG {Vertically opposite angles}
∠U = ∠G {Given}
Answer: ΔTUV ~ ΔTGH by AA similarity.
5) In ΔWVU & ΔWFG,
∠VWU = ∠FWG {Vertically opposite angles}
∠V = ∠F = 51°
Answer: ΔWVU ~ ΔWFG by AA similarity.
6) ΔUVV and ΔUQR are not similar triangles.
