Question

3 - 9 practice online
geometry (s1 p01 rm h216) sharp, jeffrey / unit 3 - similarity / lesson 3 - 9 conditions for triangle similarity
which of the following explains whether these parallelograms are similar?
the parallelograms might be similar. since we do not know if the corresponding sides are proportional, we do not know for sure if the parallelograms are similar.
the parallelograms must be similar. since we know the corresponding sides are proportional, we know for sure the parallelograms are similar.
the parallelograms might be similar. since we do not know if the corresponding angles are congruent, we do not know for sure if the parallelograms are similar.
the parallelograms must be similar. since we know the corresponding angles are congruent, we know for sure the parallelograms are similar.

Explanation:

Step1: Recall the condition for similarity of parallelograms

For two parallelograms to be similar, both the corresponding sides must be proportional and the corresponding angles must be congruent.

Step2: Check the side - proportion

For the first parallelogram \(ABCD\), \(AB = 2\), \(BC=6\), \(CD = 2\), \(DA=6\). For the second parallelogram \(WXYZ\), \(WX = 3\), \(XY = 9\), \(YZ=3\), \(ZW = 9\). The ratio of corresponding sides: \(\frac{AB}{WX}=\frac{2}{3}\), \(\frac{BC}{XY}=\frac{6}{9}=\frac{2}{3}\), \(\frac{CD}{YZ}=\frac{2}{3}\), \(\frac{DA}{ZW}=\frac{6}{9}=\frac{2}{3}\). So the corresponding sides are proportional.

Step3: Check the angle - congruence

We know that in a parallelogram, opposite angles are equal. But we have no information given about the measures of the angles of the two parallelograms. So we cannot confirm if the corresponding angles are congruent.

Answer:

The parallelograms might be similar. Since we do not know if the corresponding angles are congruent, we do not know for sure if the parallelograms are similar.