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
[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
∵ A = (0 , 0) , B = (1 , 3)
∴ AB = [tex]\sqrt{(1-0)^{2}+(3-0)^{2}}=\sqrt{1+9}=\sqrt{10}[/tex]
∵ F = (8 , 4) , E = (7 , 1)
∴ FE = [tex]\sqrt{(7-8)^{2}+(1-4)^{2}}=\sqrt{1+9}=\sqrt{10}[/tex]
∴ 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
