Question

7 as shown in the figure, it is given that m∠bad = m∠cae. which of the following statements, when added, is still not enough to deduce that △abc ~ △ade? a. m∠c = m∠e b. m∠b = m∠ade c. ab/ad = ac/ae d. ab/ad = bc/de 8 given that vw/vx = vz/vy, prove wz || xy.

Explanation:

Step1: Recall similarity - criteria for triangles

Two triangles $\triangle ABC$ and $\triangle ADE$ are similar if:

1. AA (Angle - Angle) similarity: Two pairs of corresponding angles are equal.
2. SAS (Side - Angle - Side) similarity: The ratios of two pairs of corresponding sides are equal and the included angles are equal.

We know that $\angle BAD=\angle CAE$, so $\angle BAD+\angle DAC=\angle CAE + \angle DAC$, which means $\angle BAC=\angle DAE$.

Step2: Analyze option A

If $m\angle C = m\angle E$, and we already have $\angle BAC=\angle DAE$, then by AA - similarity, $\triangle ABC\sim\triangle ADE$.

Step3: Analyze option B

If $m\angle B=m\angle ADE$, and $\angle BAC=\angle DAE$, then by AA - similarity, $\triangle ABC\sim\triangle ADE$.

Step4: Analyze option C

If $\frac{AB}{AD}=\frac{AC}{AE}$ and $\angle BAC = \angle DAE$, then by SAS - similarity, $\triangle ABC\sim\triangle ADE$.

Step5: Analyze option D

The ratio $\frac{AB}{AD}=\frac{BC}{DE}$ does not satisfy either the AA or SAS similarity criteria. The sides are not in the correct proportion for the included - angle relationship.

Answer:

D. $\frac{AB}{AD}=\frac{BC}{DE}$