Question

In Fig. 8.42, X is any point within a square
ABCD. On AX a square AXYZ is described.
Prove that BX = DZ​

Answer 1

Answer:

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Answer 2

Given:

AXYZ is a square

ABCD is a square

Prove:

BX = DZ

Proof:

In triangles BAX and ZAD,

ZA = AX {side of square AXYZ}

angle BAX= angle ZAD

AD = AB {side of square ABCD}

Let angle XAD=x

angle ZAD + x= 90° {angles in a square equal 90°}

angle ZAD= x-90° {equation 1}

angle BAX + x= 90° {angles in a square equal 90°}

angle BAX= 90°-x {equation 2}

From equations 1 and 2,

angle BAX= angle ZAD

From SAS congruence rule,

triangles BAX and ZAD are congruent

By Congruent Parts Of Corresponding Triangles {CPCT},

BX=DX

Hence proved