Congruent Triangles Maths Tuition: Solution

congruent-maths-tuition

Solution:

BS=BE+ES=ST+ES=ET

\angle DES=\angle ESA=90^\circ

BA=DT (given)

Thus, \triangle ASB is congruent to \triangle DET (RHS)

Hence \angle DTE=\angle SBA

Thus DT//BA (alt. angles)

(Proved)

By Pythagoras’ Theorem, we have

\begin{array}{rcl}DB&=&\sqrt{DE^2+BE^2}\\    &=&\sqrt{SA^2+ST^2}\\    &=&TA    \end{array}

Hence \triangle DEB and \triangle AST are congruent (SSS).

Hence \angle DBE=\angle STA

Thus DB//TA (alt. angles)

Therefore, ABDT is a parallelogram since it has two pairs of parallel sides.

(shown)