Question

1. given: d is the mid - point of segment ba and e is the mid - point of segment bc. which of the following statements is/are true? de = 1/2 ac de ii ac (ii means parallel) ∠bde ≅ ∠dac all of the above 5.4

Explanation:

Step1: Mid - point theorem application

In $\triangle ABC$, since $D$ is the mid - point of $BA$ and $E$ is the mid - point of $BC$, by the mid - point theorem, $DE\parallel AC$ and $DE=\frac{1}{2}AC$.

Step2: Corresponding angles property

Because $DE\parallel AC$, corresponding angles are equal. $\angle BDE$ and $\angle DAC$ are corresponding angles for the parallel lines $DE$ and $AC$ with transversal $BA$. So, $\angle BDE\cong\angle DAC$.

Answer:

D. All of the above