Answer: 42 cm
Step-by-step 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 [tex]=9+12+9+12=42\ cm[/tex]
- 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.
