# Calculate angle DPA (Congruent and Similar triangles)

What i tried

Drawing a line from A to E, calling it line AE, we can see 2 triangles that are simillar, triangle AEC and triangle FED. And due to this property of simillar triangles, this imply that Length ED is the same length as CE, thus length ED is also 20.9cm. Since length EP is half that of length EF, length EP is 3cm. Length DP is then 4cm due to Pythagoras theorem. Thus with length ED, EP and DP known, we cam find angle P through the Cosine rule.

Am i correct could anyone please explain. Thanks

## 1 Answer

Guide:

• Observe that $AD$ and $DP$ are perpendicular to each other, hence $\triangle ADP$ is a perpendicular triangle.

• Triangle $DEP$ and triangle $ABC$ are congruent, hence we should be able to compute the height $DP$. You have computed $DP$ correctly.

• Observe that $BE$ and $BC$ are perpenduclar to each other, hence $\triangle EBC$ is a perpendicular triangle. Hence, we can use Pythagoras theorem to compute $BE$, and we know $BE$ shares the same length as $AD$.

• We know $AD$, we know $DP$, and we know that $\angle ADP$ is $\frac{\pi}2$. We should be able to compute $\angle DPA$.

Remark:

• I don't think triangle $AEC$ and triangle $FED$ are similar. Also, note that $ED$ can't be $20.9$, it is just $5$.
• Okay i got it. Thanks for your help – ys wong Jul 11 '18 at 3:50