Question

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. StartFraction Q R Over T U EndFraction = StartFraction P R Over S U EndFraction = StartFraction P Q Over S T EndFraction = StartFraction StartRoot 52 EndRoot Over StartRoot 13 EndRoot EndFraction = Therefore, △PQR ~ △STU by the theorem.

Answer 1

Answer:

qr/tu---2

pr/su---2

pq/st= 52/13---2

Therefore, △PQR ~ △STU by the SSS similarity theorem.

Answer 2

Answer:

The answer is below

Step-by-step explanation:

Two triangles are said to be similar if their corresponding angles are equal and the corresponding sides are in proportion.

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

$Distance=\sqrt{(x_2-x_1}^2+(y_2-y_1)^2 \\\\Therefore\ in\ triangle\ PQR:\\\\|QR|=\sqrt{(-2-(-2))^2+(4-0)^2}=4\\\\|PQ|=\sqrt{(-2-4)^2+(0-4)^2}=\sqrt{52}=2\sqrt{13} \\\\|PR|=\sqrt{(-2-4)^2+(4-4)^2}=6$

In triangle STU:

$|ST|=\sqrt{(-1-2)^2+(-2-(-4))^2}=\sqrt{13}\\\\|SU|=\sqrt{(-1-2)^2+(-4-(-4))^2} =3\\\\|TU|=\sqrt{(-1-(-1))^2+(-4-(-2))^2}=2$

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

|PR| / |SU| = 6/3 = 2

|PQ| / |ST| = 2√13 / √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.