Question

which statement is not used to prove that δabc is similar to δade? ac is a transversal line passing ed and cb. angle a is congruent to itself, due to the reflexive property. segments ed and cb are parallel. the sum of angles a and b are supplementary to angle c.

Explanation:

Step1: Recall similarity - criteria

To prove two triangles $\triangle ABC$ and $\triangle ADE$ are similar, we can use AA (angle - angle), SAS (side - angle - side) or SSS (side - side - side) similarity criteria.

Step2: Analyze each statement

1. If $AC$ is a transversal line passing $ED$ and $CB$ and $ED\parallel CB$, then we can get corresponding angles equal. For example, $\angle AED=\angle ACB$ (corresponding angles), which helps in AA similarity.
2. $\angle A$ is congruent to itself (reflexive property). This is an important angle - equality for AA similarity.
3. If segments $ED$ and $CB$ are parallel, we can get angle - equalities as mentioned above, which is useful for similarity proof.
4. The statement "The sum of angles $A$ and $B$ are supplementary to angle $C$" is the angle - sum property of a triangle ($\angle A+\angle B+\angle C = 180^{\circ}$) and it is not directly used to prove the similarity of $\triangle ABC$ and $\triangle ADE$.

Answer:

The sum of angles $A$ and $B$ are supplementary to angle $C$.