Triangle lmn has coordinates l (0, 0), m (0, -2), and n (2, 0). if δlmn ≅ δxyz, what is the measure of xz?

1 unit
2 units
3 units
4 units

The measure of XZ is 2 units

Since the triangle ΔLMN ≅ ΔXYZ, hence;

Get the distance MN from the given coordinates.

LN = √0-(-2)² + (0-0)²

LN = √4

LN= 2 units

Since the measure of LN is equal to XZ, hence the measure of XZ is 2 units

Learn more on similar triangles here: link

Check the picture below.

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.