Answer:
The triangles are not congruent
Step-by-step explanation:
we know that
If two triangles are congruent, then its corresponding sides and its corresponding angles are congruent
so
If YXZ≅MNP
then
YX≅MN
XZ≅NP
YZ≅MP
Verify if the length sides are congruent
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
step 1
Find the length side YX
we have
Y (-1,3), X (-3,0)
substitute
[tex]d=\sqrt{(0-3)^{2}+(-3+1)^{2}}[/tex]
[tex]d=\sqrt{(-3)^{2}+(-2)^{2}}[/tex]
[tex]d_Y_X=\sqrt{13}\ units[/tex]
step 2
Find the length side MN
we have
M (0,-3), N (-3,-1)
substitute
[tex]d=\sqrt{(-1+3)^{2}+(-3-0)^{2}}[/tex]
[tex]d=\sqrt{(2)^{2}+(-3)^{2}}[/tex]
[tex]d_M_N=\sqrt{13}\ units[/tex]
so
YX≅MN ----> is correct
step 3
Find the length side XZ
we have
X (-3,0), and Z(-4,3)
substitute
[tex]d=\sqrt{(3-0)^{2}+(-4+3)^{2}}[/tex]
[tex]d=\sqrt{(3)^{2}+(-1)^{2}}[/tex]
[tex]d_X_Z=\sqrt{10}\ units[/tex]
step 4
Find the length side NP
we have
N (-3,-1), and P(-2,-4)
substitute
[tex]d=\sqrt{(-4+1)^{2}+(-2+3)^{2}}[/tex]
[tex]d=\sqrt{(-3)^{2}+(1)^{2}}[/tex]
[tex]d_N_P=\sqrt{10}\ units[/tex]
so
XZ≅NP ----> is correct
step 5
Find the length side YZ
we have
Y (-1,3), and Z(-4,3)
substitute
[tex]d=\sqrt{(3-3)^{2}+(-4+1)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(-3)^{2}}[/tex]
[tex]d_Y_Z=\sqrt{9}=3\ units[/tex]
step 6
Find the length side MP
we have
M (0,-3), and P(-2,-4)
substitute
[tex]d=\sqrt{(-4+3)^{2}+(-2-0)^{2}}[/tex]
[tex]d=\sqrt{(-1)^{2}+(-2)^{2}}[/tex]
[tex]d_M_P=\sqrt{5}\ units[/tex]
so
YZ≅MP -----> is not true
therefore
The triangles are not congruent
