Question

Given: triangle XYZ, segment XY is congruent to segment ZY, and YW bisects angle XYZ. Prove that angle YWZ is a right angle.

Answer 1

Step-by-step explanation:

YW bisects the angle XYZ ------(given)

considering Δ XYZ segment XY≅YZ --------given.

∠X≅∠Z angles of opposite equal sides are equal

a triangle having two equal sides is an isosceles triangle. Isosceles triangles have one 90 degrees angles as the total sum of the three angles of a triangle must equal 180 degrees.Therefore ∠Y=90 degrees

but segment YW bisects the angle Y so ∠ZYW= 45 degrees but ∠Z=45 degrees --------(ΔXYZ is a right angled isosceles triangle)

so ∠YWZ=90 degrees as ΔYWZ is also right angled isoseles triangle having two sides equal to 45 and third = 90 degrees.

Hence segmnet YW is perpendicular on segment XZ