Question

geometry: unit 3 lesson 7 practice problems

1. sketch a figure that is similar to this figure. label side and angle measures.

(figure with side length 12, angles 30°, 150°, 150°, 30°)

Explanation:

Step1: Recall Similar Figures Rule

Similar figures have equal corresponding angles and proportional sides. The given figure has angles \(30^\circ\), \(150^\circ\), \(30^\circ\), \(150^\circ\) and sides of length 12 (all equal here, so it's a rhombus - like parallelogram).

Step2: Choose a Scale Factor

Let's pick a scale factor, say \(k = 2\). So new side length \(= 12\times2 = 24\). Angles remain \(30^\circ\), \(150^\circ\), \(30^\circ\), \(150^\circ\) (since angles are preserved in similar figures).

Step3: Sketch the New Figure

Draw a parallelogram (since opposite sides and angles are equal) with side length 24, angles \(30^\circ\) and \(150^\circ\) at corresponding vertices. Label sides as 24 and angles as \(30^\circ\), \(150^\circ\), \(30^\circ\), \(150^\circ\). (Alternatively, use any positive scale factor \(k
eq1\); if \(k = \frac{1}{2}\), side length \(= 6\), same angles.)

Answer:

A similar figure can be a parallelogram with side length \(12k\) (where \(k\) is a positive real number, e.g., \(k = 2\) gives side length 24) and angles \(30^\circ\), \(150^\circ\), \(30^\circ\), \(150^\circ\) (sketched with these side and angle measures labeled).