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.

Answer 1

Answer:

See Explanation

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).

• We know, 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:

IQRI = $\sqrt{(-2_{}-(-2)_{})^{2} + (4_{}-0_{})^{2} }$ = 4

IPQI = $\sqrt{(-2_{}-4_{})^{2} + (0_{}-4_{})^{2} }$ = √52

IPRI = $\sqrt{(-2_{}-4_{})^{2} + (4_{}-4_{})^{2} }$ = 6

• Now Similarly, In triangle STU

ISTI = $\sqrt{(-1_{}-2_{})^{2} + (-2_{}-(-4)_{})^{2} }$ = √13

ISUI = $\sqrt{(-1_{}-2_{})^{2} + (-4_{}-(-4)_{})^{2} }$ = 3

ITUI = $\sqrt{(-1_{}-(-1)_{})^{2} + (-4_{}-(-2)_{})^{2} }$ = 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.