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? ode = 1/2ac ode ii ac (ii means parallel) o∠bde≅∠dac oall 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, the line segment joining the mid - points of two sides of a triangle is parallel to the third side and half its length. So, $DE=\frac{1}{2}AC$ and $DE\parallel AC$.

Step2: Angle - angle similarity

Since $DE\parallel AC$, $\angle BDE$ and $\angle DAC$ are corresponding angles. For two parallel lines $DE$ and $AC$ with transversal $BA$, corresponding angles are equal. So, $\angle BDE\cong\angle DAC$.

Answer:

D. All of the above