Question

Prove that the digonals of isosceles trapizium are equal.​

Answer 1

consider the isosceles trapezium, ABCD

where:

AD||BC

AB=CD

angle BAD = angle CDA { a given condition,ABCD is an isosceles trapezium}

the diagonals AC and BD create two triangles

triangle ABD and triangle ACD

the two triangle are congruent (SAS)

justification

• [S] AB=CD

• [A] angle BAD = angle CDA

• [S] AD = DA { Common side }

therefore. the corresponding side of the two triangles BD and AC are also congruent.

{ the two diagonals of the trapezium,as required}