Ask Singapore Homework?
Upload a photo of a Singapore homework and someone will email you the solution for free.
Question
secondary 4 | A Maths
One Answer Below
Anyone can contribute an answer, even non-tutors.
Hello! How do i solve this question?
AB = BC
So triangle ABC is isosceles.
Angle ACB = angle CAB
(Base angles of an isosceles triangle)
Since angle ABD = angle ACB, then
angle ABD = angle CAB
And angle CAB and angle DAB are common.
So angle DAB = angle ABD, which means triangle ADB is isosceles.
Therefore AD = BD ( the legs of an isosceles triangles are equal)
①angle ABD = angle ACB (given)
②angle CAB = angle DAB (common angle)
By AA similarity, triangle ABD is similar to triangle ACB.
From the above, we can deduce that :
AD = BD = y cm
AB = BC = x cm
Since the two triangles are similar, and the ratio of their corresponsing sides = AB/AD = x/y ,
Then the ratio of their areas (area ACB/area ABD) is the square of the ratio of their corresponding sides
= x²/y²
See 1 Answer