Question

In figure 3.48, point A is on the bisector of ∠XYZ. If AX=2 cm then find AZ.

Answer 1

Ay is the bisector of <xyz

so, <ayx = <ayz .......(1)

In tri.ayx and tri.ayz

<axy = < azy (each of 90°)
Ay =Ay (common )
<ayx = <ayz (from eq.1 )

tri.ayx is congruent tri.ayz (AAS similarity )
AX = AZ ( By C.P.C.T.C )
AX =2 cm
and AX =AZ = 2 CM
HENCE ,AZ = 2 Cm

Answer 2

Answer:

In figure 3.48, point A is on the bisector of ∠XYZ. If AX=2 cm

then AZ = 2 cm

Step-by-step explanation:

in Δ YAX & ΔYAZ

∠AYX =  ∠AYZ   ( bisector of ∠XYZ)

∠AXY = ∠AZY = 90° ( given)

∠YAX = ∠YAZ   ( as other two angles are equal and sum of three angles = 180°)

Δ YAX ≅ ΔYAZ

YA /YA  =  AX/AZ   =  YX/YZ

=> 1 = AX/AZ

=> AZ = AX

=> AZ = 2 cm