On a coordinate plane, triangles P Q R and S T U are shown. Triangle P Q R has points (4, 4), (negative 2, 0), (negative 2, 4). Triangle S T U has points (2, negative 4), (negative 1, negative 2), (negative 1, negative 4). Complete the statements to verify that the triangles are similar.

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Step-by-step explanation:

According to The Question,

Given That, On a coordinate plane, ΔPQR and ΔSTU are shown. ΔPQR has points (4,4) , (-2,0) , (-2,4). ΔSTU has points (2,-4) , (-1,-2) , (-1,-4).

The distance between two points on the coordinate plane is given as:

Distance =

IQRI = = 4

IPQI = = √52

IPRI = = 6

ISTI = = √13

ISUI = = 3

ITUI = = 2

Now, Verifying that the triangles are similar  

|QR| / |TU| = 4/2 = 2

|PR| / |SU| = 6/3 = 2  

|PQ| / |ST| = √52 / √13 = 2

Hence,   |QR| / |TU| = |PR| / |SU| = |PQ| / |ST|

Therefore, △PQR and △STU are similar triangles since the ratio of their sides are in the same proportion.

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