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If ΔYWZ ~ ΔYXW, what is true about XWZ?

A. XWZ is an obtuse angle.

B. XWZ is a right angle.

C. XWZ is congruent to WXY.

D. XWZ is congruent to XZW.

If ΔYWZ ΔYXW what is true about XWZA XWZ is an obtuse angleB XWZ is a right angleC XWZ is congruent to WXYD XWZ is congruent to XZW class=

Respuesta :

frika

If [tex] \triangle YWZ \sim \triangle YXW [/tex], then

[tex] \angle YWZ\cong \angle YXW,\\\angle WYZ\cong \angle XYW,\\\angle WZY\cong \angle XWY. [/tex]

Consider angle XWZ:

[tex] m\angle XWZ=m\angle XWY+m\angle YWZ [/tex].

Since [tex] \angle YWZ\cong \angle YXW, [/tex], then

[tex] m\angle XWZ=m\angle XWY+m\angle YWZ=m\angle XWY+m\angle YXW\ \ (*) [/tex].

Now consider the right triangle XWY. The sum of measures of all angles of triangle is equal to 180°, so

[tex] m\angle XWY+m\angle WXY+m\angle WYX=180^{\circ},\\m\angle XWY+m\angle WXY=180^{\circ}-m\angle WYX=180^{\circ}-90^{\circ}=90^{\circ}. [/tex]

Substitute this expression into expression (*):[tex] m\angle XWZ=90^{\circ} [/tex].

Answer: correct choice is B.

Two triangle are congruent when the shape and size of both the triangle are same.

The given triangles [tex]\Delta YWZ \cong\Delta YXW[/tex] are congruent.

What is triangle congruence theorem?

Two triangle are congruent when the shape and size of both the triangle are same.

Triangle congruence theorem are-

  • Angle-Side-Angle theorem (AAS)- This theorem states that two triangle is congruent when two angle and one side of the triangle are respectively equal to the two angles and same side of the other triangle.
  • Side-Side-Side theorem (SSS)- When the three sides of the one triangle is equal to the three sides of the other triangle respectively, then the triangle are congruent.
  • Side-Angle-Side theorem (SAS)- Two sides and the included angle of are equal to the two sides and one angle of other triangle respectively.

Thus the,

[tex]\angle YZW \cong \angle YXW\\\angle WYZ \cong \angle WYX\\\angle ZWY \cong \angle XWY[/tex]

As,

[tex]\angle XWZ= \angle XWY+\angle YWZ=\angle XWY+\angle YXW[/tex]

In [tex]\Delta XWZ[/tex], the sum of all the angle of a triangle is 180 degree. Thus,

[tex]\angle YZW +\angle YXW+\angle ZWX=180[/tex]

As the angle [tex]\angle YZW = \angle YXW[/tex]. thus,

[tex]\angle XWY+\angle WXY=180-\angle WYZ\\\angle XWY+\angle WXY=180-90=90[/tex]

thus the [tex]\angle XWZ[/tex] is a right angle. The option B is the correct option.

Learn more about the congruence theorem here;

https://brainly.com/question/19258025

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