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son4ous [18]
3 years ago
9

HELP++++++++++++++++++++++++

Mathematics
1 answer:
lys-0071 [83]3 years ago
3 0

Answer:

ASA

ΔFGH ≅ ΔIHG ⇒ answer B

Step-by-step explanation:

* Lets revise the cases of congruence  

- SSS  ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ

- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and  

 including angle in the 2nd Δ

- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ  

 ≅ 2 angles and the side whose joining them in the 2nd Δ

- AAS ⇒ 2 angles and one side in the first triangle ≅ 2 angles  

 and one side in the 2ndΔ  

- HL ⇒ hypotenuse leg of the first right angle triangle ≅ hypotenuse

 leg of the 2nd right angle Δ

* Lets prove the two triangles FGH and IHG are congruent by on of

 the cases above

∵ FG // HI and GH is transversal

∴ m∠FGH = m∠IHG ⇒ alternate angles

- In the two triangles FGH and IHG

∵ m∠FHG = m∠IGH ⇒ given

∵ m∠FGH = m∠IHG ⇒ proved

∵ GH = HG ⇒ common side

∴ ΔFGH ≅ ΔIHG ⇒ ASA

* ASA

 ΔFGH ≅ ΔIHG

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