Question

Given ΔCAB ≅ ΔEDF, complete the sentences below. In ΔCAB, the measure of line BC is 4 units, and the measure of line AC is 5 units. In ΔEDF, the measure of line DE is 3x + 2 units, the measure of line EF is y units, and the measure of Line DF is 2x + y units.

The measure of line DE is __ units.



The measure of line EF is __ units.



The measure of line DF is __ units.

Answer 1

Answer: The measure of line DE is 5 units.

The measure of line EF is 4 units.

The measure of line DF is 6 units.

Explanation:

Given: ΔCAB ≅ ΔEDF

By CPCTC, corresponding sides both triangle are congruent.

Therefore

AC=DE.....(1),

AB=DF...(2),

BC=EF.........(3)

From (1),

DE=5 units

`\\\Rightarrow5=3x+2\\\Rightarrow\ 3x=5-2\\\Rightarrow\ 3x=3\\\Rightarrow\ x=1`

From (3)

EF=4 units

⇒ y= 4units

Now, DF= 2x+y=2(1)+4=6 units

Therfore, from (2), AB= 4 units.