#### Monoxdifly

The triangle ABC is a right triangle with A as the right angle and BD is the bisector of angle B. If AB = 12 cm and BC = 15 cm, the length of AD is ....
A. 3 cm
B. 4 cm
C. 5 cm
D. 6 cm
It was a question for a 9th grader and the book hasn't covered trigonometry by name yet (As in, they don't know about the term sine, cosine, and tangent, but the books do explain the length ratio of triangle which has 45°-90°-45° angle or 30°-60°-90° angle. How to do it and explain it to them?

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#### Idea

1) Extend CB to E such that AB=BE=12
2) Show AE parallel to DB
3) use ratios

topsquark

#### Cervesa

$\Delta DAB \cong \Delta DCB$

use Pythagoras with $\Delta CDE$ to solve for $x=|AD|$

#### Cervesa

should be $\Delta DAB \cong \Delta DEB$

topsquark

#### Monoxdifly

Thank you, both of you!

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