Question

self - assessment

1. in the diagram, $\triangle jkl \sim \triangle pqr$.

a. find the scale factor from $\triangle jkl$ to $\triangle pqr$.
b. list all pairs of congruent angles.
c. write the ratios of the corresponding side lengths in a statement of proportionality.

Explanation:

Part a:

Step1: Identify corresponding sides

In similar triangles \( \triangle JKL \) and \( \triangle PQR \), the corresponding sides are \( JK \) and \( PQ \), \( KL \) and \( QR \), \( JL \) and \( PR \). From the diagram, \( JK = 6 \), \( KL = 4 \), \( JL = 8 \); \( PQ = 9 \), \( QR = 6 \), \( PR = 12 \).

Step2: Calculate scale factor

The scale factor from \( \triangle JKL \) to \( \triangle PQR \) is the ratio of corresponding sides. Let's take \( JK \) and \( PQ \): \( \text{Scale Factor} = \frac{PQ}{JK}=\frac{9}{6}=\frac{3}{2} \). We can verify with other sides: \( \frac{QR}{KL}=\frac{6}{4}=\frac{3}{2} \), \( \frac{PR}{JL}=\frac{12}{8}=\frac{3}{2} \).

For similar triangles, corresponding angles are congruent. In \( \triangle JKL \sim \triangle PQR \), the corresponding angles are \( \angle J \) and \( \angle P \), \( \angle K \) and \( \angle Q \), \( \angle L \) and \( \angle R \).

For similar triangles \( \triangle JKL \) and \( \triangle PQR \), the ratios of corresponding side lengths (statement of proportionality) are formed by taking the ratio of each pair of corresponding sides. The corresponding sides are \( JK \) & \( PQ \), \( KL \) & \( QR \), \( JL \) & \( PR \).

Answer:

The scale factor from \( \triangle JKL \) to \( \triangle PQR \) is \( \frac{3}{2} \).

Part b: