Similar Triangles
They can be identified because they satisfy the following conditions:
* All of their corresponding side lengths are proportional
* All of their corresponding internal angles are congruent (have the same measure).
There are four choices with measurements to prove triangles MPQ and NPR are similar.
The correct choice is that where the ration of the side lengths PN:PM is equal to the proportion of the side lengths PR:PQ
Let's test them:
(1)
PN:PM= 10:12. Simplifying: PN:PM= 5:6
PR:PQ= 18:20 = 9:10
The scale factor is not the same, so this choice is not correct.
(2)
PN:PM= 8:16=1:2
PR:PQ= 10:15=2:3
The scale factor is not the same, so this choice is not correct.
(3)
PN:PM= 12:16=3:4
PR:PQ= 15:25=3:5
The scale factor is not the same, so this choice is not correct.
(4)
PN:PM= 6:9=2:3
PR:PQ= 8:12=2:3
Since both ratios are equal, this choice describes the measures of similar triangles.
Answer: Choice 4