Question

In figure, ∆ABC is a right angled triangle at B. ADEC and BCFG are squares. Prove that AF = BE

Answer 1

Given : In right angle ∆ ABC , Angle B = 90°

ADEC and BCFG are squares on the sides AC and BC of triangle ABC respectively AF and BE are joined

To prove : AE = BE

angle ACE = angle BCF

adding angle ACB both side

angle ACE +angle ACB = angle BCF + angle ACB
angle BCE = angle ACF

in ∆ BCE and ∆ACF

BC = CF ( square sides)

CE = AF ( square sides)

angle BCE = angle ACF

∆ BCD and ∆ ACF are congruent triangle

BE= AF ( by cpct )

HP

Answer 2

Step-by-step explanation:

Given : In right angle ∆ ABC , Angle B = 90°

ADEC and BCFG are squares on the sides AC and BC of triangle ABC respectively AF and BE are joined

To prove : AE = BE

angle ACE = angle BCF

adding angle ACB both side

angle ACE +angle ACB = angle BCF + angle ACB

angle BCE = angle ACF

in ∆ BCE and ∆ACF

BC = CF ( square sides)

CE = AF ( square sides)

angle BCE = angle ACF

∆ BCD and ∆ ACF are congruent triangle

BE= AF ( by cpct )