Question

1. △pqr is similar to △def as shown below. which describes the relationship between the corresponding sides of the two triangles? a. \\(\frac{pq}{de}=\frac{6}{4}\\) b. \\(\frac{pr}{de}=\frac{6}{6}\\) c. \\(\frac{pq}{de}=\frac{4}{6}\\) d. \\(\frac{pq}{ef}=\frac{4}{9}\\) 5. in the diagram below, △sml ~ △big. what is the length of \\(\overline{bi}\\)? a. 35 cm b. 40 cm c. 26 cm d. 30 cm 6. figures that have the same shape but are different sizes are: a. reflexive property b. dilation c. congruent d. similar

Explanation:

Step1: Recall property of similar triangles

For similar triangles, the ratios of corresponding sides are equal. In $\triangle PQR\sim\triangle DEF$, $PQ$ corresponds to $DE$, $PR$ corresponds to $DF$ and $QR$ corresponds to $EF$. Given $PQ = 4$ cm and $DE=6$ cm, so $\frac{PQ}{DE}=\frac{4}{6}$.

Step2: Solve for side - length in similar triangles (for question 5)

Since $\triangle SML\sim\triangle BIG$, the ratio of corresponding sides is the same. $\frac{SM}{BI}=\frac{SL}{BG}$. We know $SM = 10$ cm, $SL = 16$ cm and $BG=56$ cm. Let $BI=x$. Then $\frac{10}{x}=\frac{16}{56}$, cross - multiply gives $16x=10\times56$, so $x=\frac{10\times56}{16}=35$ cm.

Step3: Recall definition of similar figures

Figures that have the same shape but different sizes are called similar.

Answer:

1. C. $\frac{PQ}{DE}=\frac{4}{6}$
2. A. 35 cm
3. D. similar