Question

State if the two triangles are congruent. If they are state the condition of their
congruency​

Answer 1

Answer:

All the given triangles are congruent

(a) Δ ABC ≅ Δ DCA

• AB = DC (Given)
• <DAC = <BCA (Given)

• AC = AC (Common)

Therefore, according to SAS congruency criteria, Δ ABC ≅ Δ DCA.

(b) Δ ABC ≅ Δ ACD

• <BAC = <DCA (Given)
• <DAC = <BCA (Given)
• AC = AC (Common)

Therefore, according to ASA congruency criteria, Δ ABC ≅ Δ ACD.

(c) Δ ABC ≅ Δ BCD

• AB = BC (Given)
• AC = CD (Given)
• BC = BC (Common)

Therefore, according to SSS congruency criteria, Δ ABC ≅ Δ BCD.

(d)  Δ ABC ≅ Δ EDC

• <BAC = <DEC (Should have been Given)

• <ACB = <DCE (Vertically opposite Angles)
• AC = CE (Given)

Therefore, according to ASA congruency criteria, Δ ABC ≅ Δ EDC.

(e)  Δ ABC ≅ Δ DEF

• Both are Right Angled Triangles

• <ACB = <EFD (Given)
• AB = DE (Given)

Therefore, according to RHS congruency criteria, Δ ABC ≅ Δ DEF.  

(f)  Δ ABC ≅ Δ EDC

• <ABC = <EDC (Given)

• <BCA = <DCE (Vertically opposite Angles)
• BC = CD (Given)

Therefore, according to ASA congruency criteria, Δ ABC ≅ Δ EDC.

Hope this helps you!

Answer 2

Answer:

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