1
$\begingroup$

In the following figure, we have two right triangles, ABC and BDC. Knowing that triangle BDC is isosceles (BD=DC) show that the measure of angle DAC is 45 degrees.enter image description here

I'm not even sure where to start with this one. Any help would be greatly appreciated!

$\endgroup$
1
$\begingroup$

Trace the circle whose diameter is the common hypothenuse $BC$. The angles $BAD$ and $DAC$ are both on this circumference and correspond to chords that have equal length ($BD$ and $CD$), so they are equal. Since their sum is $\frac{\pi}{2}$, they both have to be $\frac{\pi}{4}$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.