Mathematics: Triangle yxz has coordinates at y (-1,3), x (-3,0), and z(-4,3) and triangle mnp has coordinates at m (0,-3), n (-3,-1), and p(-2,-4). are the two triangles congruent?

B.) (2, 6) (-2, -6) (2, -6) (-2, 6)Good luck love ~...

Triangle yxz has coordinates at y (-1,3), x (-3,0),

Ответ:

Theresab2021

16.01.2022

Mathematics

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

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

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

step 1

Find the length side YX

we have

Y (-1,3), X (-3,0)

substitute

$d=\sqrt{(0-3)^{2}+(-3+1)^{2}}$

$d=\sqrt{(-3)^{2}+(-2)^{2}}$

$d_Y_X=\sqrt{13}\ units$

step 2

Find the length side MN

we have

M (0,-3), N (-3,-1)

substitute

$d=\sqrt{(-1+3)^{2}+(-3-0)^{2}}$

$d=\sqrt{(2)^{2}+(-3)^{2}}$

$d_M_N=\sqrt{13}\ units$

YX≅MN ----> is correct

step 3

Find the length side XZ

we have

X (-3,0), and Z(-4,3)

substitute

$d=\sqrt{(3-0)^{2}+(-4+3)^{2}}$

$d=\sqrt{(3)^{2}+(-1)^{2}}$

$d_X_Z=\sqrt{10}\ units$

step 4

Find the length side NP

we have

N (-3,-1), and P(-2,-4)

substitute

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

$d=\sqrt{(-3)^{2}+(1)^{2}}$

$d_N_P=\sqrt{10}\ units$

XZ≅NP ----> is correct

step 5

Find the length side YZ

we have

Y (-1,3), and Z(-4,3)

substitute

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

$d=\sqrt{(0)^{2}+(-3)^{2}}$

$d_Y_Z=\sqrt{9}=3\ units$

step 6

Find the length side MP

we have

M (0,-3), and P(-2,-4)

substitute

$d=\sqrt{(-4+3)^{2}+(-2-0)^{2}}$

$d=\sqrt{(-1)^{2}+(-2)^{2}}$

$d_M_P=\sqrt{5}\ units$

YZ≅MP -----> is not true

therefore

The triangles are not congruent

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Triangle yxz has coordinates at y (-1,3), x (-3,0), and z(-4,3) and triangle mnp has coordinates at m (0,-3), n (-3,-1), and p(-2,-4). are the two triangles congruent?

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