Question

Prove that triangle Bad is congruent to triangle ABC​

Answer 1

Explanation:

From the diagram,

i. To prove that; ΔBAD ≅ ΔABC

It can be inferred that;

<BAD ≅ <ABC (right angle of a triangle)

AC ≅ BD (diagonal of a rectangle)

AD ≅ BC (property of the sides of a rectangle)

AB ≅ CD (property of the sides of a rectangle)

Therefore,

ΔBAD ≅ ΔABC (SAS, Side-Angle-Side, congruent relations)

ii. From the given rectangle,

AC = BD = diagonal

Since;

AD ≅ BC (property of the sides of a rectangle)

AB ≅ CD (property of the sides of a rectangle)

Then,

AC ≅ BD (diagonal property of a rectangle)