Question

If ΔDEF ≅ ΔBCA, write the part(s) of ΔBCA that correspond to
(i) ∠E (ii) EF (iii) ∠F (iv) DF

Answer 1

Step-by-step explanation:

(i) ∠C

(ii) CA

(iii) ∠A

(iv) BA

Answer 2

(i) ∠E ↔ ∠C

(ii) side EF ↔ side CA

(iii) ∠F ↔ ∠A

(iv) side DF ↔ side BA

Step-by-step explanation:

Given:

ΔDEF ≅ ΔBCA

To find:

the corresponding angles and sides to the triangle BCA

Solution:

It is given that ΔDEF ≅ ΔBCA,

Hence, the corresponding angles and corresponding sides will also be congruent.

To find the corresponding angles and sides we look at the names of the triangles DEF & BCA

⇒ The angle E is positioned 2nd in the name DEF, hence its corresponding angle will be the second angle positioned in the name BCA

∴ ∠E ≅ ∠C

So, ∠E ↔ ∠C

⇒ side EF has the vertices E & F positioned second and third respectively in the name of the triangle DEF

Hence, the second and third vertices of ΔBCA are C & A respectively

The side formed will be CA

∴side EF ≅ side CA

side EF ↔ side CA

⇒ Now the angle F will correspond to the third angle of the ΔBCA because it is at the third position in the name DEF

∴ ∠F≅∠A

∠F ↔ ∠A

⇒ side DF will correspond to side BA as the position of the vertices in the name of the triangles is taken into consideration.

∴ side DF≅ side BA

side DF ↔ side BA