I entered the wrong coordinates in a previous question, i corrected down below.

Question

I entered the wrong coordinates in a previous question, i corrected down below.

How do I determine which two triangles on a graph are congruent. ∆QRS and ∆DEF or ∆ABC and ∆XYZ.
i found the coordinates of both sets:
QRS Q(-2,5), R(-2,1), S(-5, 1)
DEF D(5,-6), E(5,-2), F(2,-2)
or
ABC A(4,5), B(6,2), C(2,2)
XYZ X(-4,-5), Y(-6,-2), Z(-2,-2)
Steve replied to use the distance formula but i don't know what that is.

Answer 1

If you have two points (a,b) and (c,d)

then the distance between them is
√( (a-c)^2 + (b-d)^2 )
(notice that since we are squaring the difference, it really would not matter in which direction you are subtracting)

e.g. for R(-2,1) and S(-5,1)
RS = √( (-2+5)^2 + (1-1)^2 )
= √( 9 + 0)
= 3

Repeat for the other two segments of the first triangle and the three segments of the second triangle.
If you can find 3 equal pairs, then the triangles are congruent, since you have 3 corresponding sides equal.

Answer 2

Thanks.

I used the distance formula but i am getting that both sets are congruent but there is only one answer and I don't know what i did wrong.

Answer 3

To determine if two triangles on a graph are congruent, you can compare their respective side lengths and angles. In this case, let's consider the two sets of triangles: ∆QRS and ∆DEF, and ∆ABC and ∆XYZ.

To calculate the side lengths of triangles, you can use the distance formula. The distance formula is a formula to find the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem. The distance formula is:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Where (x₁, y₁) and (x₂, y₂) are the coordinates of two points, and d represents the distance between them.

Let's calculate the side lengths of the triangles using the distance formula:

For ∆QRS:
- The distance between Q and R is: √((-2 - (-2))² + (5 - 1)²) = 4
- The distance between R and S is: √((-2 - (-5))² + (1 - 1)²) = 3
- The distance between S and Q is: √((-5 - (-2))² + (1 - 5)²) = 5

For ∆DEF:
- The distance between D and E is: √((5 - 5)² + (-6 - (-2))²) = 4
- The distance between E and F is: √((5 - 2)² + (-2 - (-2))²) = 3
- The distance between F and D is: √((2 - 5)² + (-2 - (-6))²) = 5

For ∆ABC:
- The distance between A and B is: √((4 - 6)² + (5 - 2)²) = 3.6056
- The distance between B and C is: √((6 - 2)² + (2 - 2)²) = 4
- The distance between C and A is: √((2 - 4)² + (2 - 5)²) = 3.6056

For ∆XYZ:
- The distance between X and Y is: √((-4 - (-6))² + (-5 - (-2))²) = 3.6056
- The distance between Y and Z is: √((-6 - (-2))² + (-2 - (-2))²) = 4
- The distance between Z and X is: √((-2 - (-4))² + (-2 - (-5))²) = 3.6056

Now that we have calculated the side lengths for both sets of triangles, we can compare them. If all corresponding side lengths are equal, then the triangles are congruent.

For ∆QRS and ∆DEF:
- The side lengths are 4, 3, and 5 for both triangles.

For ∆ABC and ∆XYZ:
- The side lengths are 3.6056, 4, and 3.6056 for both triangles.

Therefore, both sets of triangles (∆QRS and ∆DEF, ∆ABC and ∆XYZ) have corresponding side lengths that are equal. Hence, both sets of triangles are congruent.