Question

An angle bisector AC divides a trapezoid ABCD into two similar triangles △ABC and △ACD. Find the perimeter of this trapezoid if the leg AB=9 cm and the leg CD=12 cm.

Answer 1

Answer: 42 cm

Explanation:

Given: An angle bisector AC divides a trapezoid ABCD into two similar triangles △ABC and △ACD.

⇒ All the corresponding angles in both triangles are congruent.

Since AC=AC [ reflexive property]

⇒ △ABC ≅△ADC [By AAS congruence theorem]

⇒AB=AD= 9 cm and BC=CD=12 cm [ By CPCTC]

Now, Perimeter of trapezoid =AB+BC+CD+AD

Perimeter of trapezoid
`=9+12+9+12=42\ cm`

• The AAS theorem says that if two angles and any side of a triangle are congruent to two angles and any side of another triangle, then these triangles are congruent.