General Mathematics · Unit 1 · Similarity and scale · Similar figures and scale factors
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Two triangles are shown in the diagram below. (a) Calculate the ratio of each pair of corresponding sides to determine whether Triangle PQR and Triangle XYZ are similar. (1 mark) (b) Justify your conclusion about whether the triangles are similar by referring to an appropriate similarity condition. (1 mark) (c) Given that Triangle PQR has an area of 54 cm², calculate the area of Triangle XYZ. (1 mark)
Two triangles, ΔABC and ΔPQR, have the following measurements: ΔABC: side lengths AB = 6 cm, BC = 9 cm, and CA = 12 cm ΔPQR: side lengths PQ = 4 cm, QR = 6 cm, and RP = 8 cm Determine whether these two triangles are similar by comparing the ratios of corresponding sides.
Two triangular garden beds are planned for a community park. Triangle PQR has sides PQ = 3.6 m, QR = 4.8 m, and angle PQR = 65°. Triangle ABC is a proposed similar design where AB = 6.3 m and BC = 8.4 m. The table shows four possible angle measurements for angle ABC. Determine which angle would make triangle ABC similar to triangle PQR, and calculate the scale factor from triangle PQR to triangle ABC.