Question

if ∠bdc≅∠bde, bc = 5p - 7, and be = 4p, what is the value of p?

Explanation:

Step1: Apply angle - side property

Since $\angle BDC\cong\angle BDE$ and $\angle BCD = \angle BED=90^{\circ}$ and $BD$ is common, by the Angle - Angle - Side (AAS) congruence criterion, $\triangle BDC\cong\triangle BDE$. Then $BC = BE$.

Step2: Set up the equation

Set up the equation $5p - 7=4p$.

Step3: Solve the equation

Subtract $4p$ from both sides: $5p-4p - 7=4p-4p$. So $p - 7=0$. Then add 7 to both sides: $p-7 + 7=0 + 7$.

Answer:

$7$