Question

(a)Find the scale factor from △ABC to △JKL.Enter the scale factor as a simplified ratio.(b)List all pairs of congruent angles

Answer 1

a) 3/4

Step-by-step explanation:

Part A

If triangles ABC and JKL are similar, then the ratio of the corresponding sides is:

`(AB)/(JK)=(BC)/(KL)=(AC)/(JL)`

Substitute the given values:

`\begin{gathered} (AB)/(JK)=(27)/(36)=(3)/(4) \\ (BC)/(KL)=(36)/(48)=(3)/(4) \\ (AC)/(JL)=(21)/(28)=(3)/(4) \end{gathered}`

Thus, the scale factor from △ABC to △JKL is 3/4.

Part B

Given that ABC and JKL are congruent, then:

`\begin{gathered} \angle A\cong\angle J \\ \angle B\cong\angle K \\ \angle C\cong\angle L \end{gathered}`