Question

Based only on the information given in the diagram, it is guaranteed that

Answer 1

Answer:

True

Step-by-step explanation:

Given

In JKL, we have:

$\angle J = 27$

$\angle K = 90$

In WXY, we have:

$\angle Y = 63$

$\angle X = 90$

Required

Is JKL ~ WXY?

In both triangles, we already have one similar angle (90)

Next, is to determine the third angles in both triangles.

In JKL

$\angle J + \angle K + \angle L = 180$

We have that:

$\angle J = 27$ and $\angle K = 90$

The expression becomes:

$27 + 90 + \angle L = 180$

$117 + \angle L = 180$

$\angle L = 180-117$

$\angle L = 63$

In WXY

$\angle W + \angle X + \angle Y = 180$

We have that:

$\angle Y = 63$ and $\angle X = 90$

The expression becomes:

$\angle W + 63 + 90 = 180$

$\angle W + 153 = 180$

$\angle W = 180-153$

$\angle W = 27$

The three angles in JKL are:

$\angle J = 27$    $\angle K = 90$   $\angle L = 63$

The three angles in WXY are:

$\angle W = 27$   $\angle X = 90$   $\angle Y = 63$

By comparing the angles, we can conclude that  both triangles are similar because of AAA postulate (Angle-Angle-Angle)