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.

Similar triangles may or may not be congruent

Triangles PQR and STU are similar by SSS theorem.

The vertices of triangle PQR are given as:

The vertices of triangle STU are given as:

Start by calculating the side lengths of the two triangles, using the following distance formula

For triangle PQR, we have:

For triangle STU, we have:

Check if the side lengths of both triangles are similar, by dividing corresponding sides

Because the scale factors of the side lengths are the same, then both triangles are similar by SSS theorem.

Read more about similar triangles at:

link

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:

In triangle STU:

|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.

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.

1. sometimes

2. never true

3. sometimes

step-by-step explanation:

these are pretty self explanatory if you know what supp right and com angles are