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: Recall mid - point theorem

In a triangle, if a line segment joins the mid - points of two sides of a triangle, then the line segment is parallel to the third side and its length is half of the length of the third side. 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: Consider angle - angle similarity

Since $DE\parallel AC$, $\angle BDE$ and $\angle BAC$ (i.e., $\angle DAC$) are corresponding angles. Corresponding angles formed by a transversal ($BA$) intersecting two parallel lines ($DE$ and $AC$) are congruent. So, $\angle BDE\cong\angle DAC$.

Answer:

All of the above