Question

BDсStatementsReasons1. AB || CDAC || BD1. GivenIf two parallel lines are cut by a transversal, then:2. ZABC ZBCDLACB LDBC2.1-13.3. Reflexive propertyI14. AACB SADBC4.IIL-:: alternate interior angles are congruent:: corresponding angles are congruent:: BD - AC:: BC – BC:: AB ~CD:: Angle-Side-Angle:: Angle-Angle-Side:: Side-Angle-Side

Answer 1

The diagram shows statements to prove that both triangles are congruent.

Hence;

$\begin{gathered} (2) \\ \angle ABC\cong\angle BCD \\ \angle ACB\cong\angle DBC \\ Alternate\text{ interior angles are congruent } \end{gathered}$$\begin{gathered} (3) \\ BC\cong BC \\ \operatorname{Re}flexive\text{ property} \end{gathered}$$\begin{gathered} (4) \\ \Delta ACB\cong\Delta DBC \\ \text{Side}-\text{Angle}-\text{Side} \end{gathered}$

Step 1 showed two sides that are congruent for both triangles

Step 2 showed two angles that are congruent

Step 3 showed two sides that are congruent

Therefore, the triangles are congruent by the side-angle-side theorem