Question

A.) a. SSS; b. SAS

Answer 1

Answer:

a. SSS; b. CPCTC ⇒ answer B

Step-by-step explanation:

* Lets explain how to solve the problem

- In the two triangles ABC and FED

∵ AD = FC ⇒ given

- By adding the common part DC to them

∴ AC = FD ⇒ (1)

∵ BC = ED ⇒ (2) (given)

- We can find the length of AB and FE by using the rule of the distance

 $d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

∵ A = (0 , 0) , B = (1 , 3)

∴ AB = $\sqrt{(1-0)^{2}+(3-0)^{2}}=\sqrt{1+9}=\sqrt{10}$

∵ F = (8 , 4) , E = (7 , 1)

∴ FE = $\sqrt{(7-8)^{2}+(1-4)^{2}}=\sqrt{1+9}=\sqrt{10}$

∴ AB = FE = √10 ⇒ (3)

- From (1) , (2) , (3)

∴ Δ ABC ≅ Δ FED by SSS

- The meaning of CPCTC is corresponding parts of congruent triangles

  are congruent.

∴ By CPCTC ∠B = ∠E

* by (a) SSS, Δ ABC ≅ Δ FED, and then ∠B = ∠E by (b) CPCTC