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secondary 4 | A Maths
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Candice
Candice

secondary 4 chevron_right A Maths chevron_right Singapore

Hello! How do i solve this question?

Date Posted: 4 years ago
Views: 191
J
J
4 years ago
i)

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)
J
J
4 years ago
ii)

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
Candice
Candice
4 years ago
Thank you for the help!
J
J
4 years ago
Hold on, editing
Candice
Candice
4 years ago
Oh ok i see oops
J
J
4 years ago
Done!
Candice
Candice
4 years ago
Thank you :)

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