Grade 8 Geometry: Unit Review

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   Triangle ABC is similar to triangle DEF. AB = 10 cm, BC = 12 cm, and DE = 15 cm. What is the length of EF, in cm?

   1. In similar triangles, corresponding sides are proportional: AB/DE = BC/EF.
   2. The scale factor from ABC to DEF is 15 ÷ 10 = 1.5 (= 3/2).
   3. EF = 12 × 15 ÷ 10 = 18 cm.

   Answer: 18

2. Example 2

   Point P(−6, −2) is reflected across the y-axis to P′. What is the x-coordinate of P′?

   1. Reflecting across the y-axis keeps y the same and changes the sign of x: (x, y) → (−x, y).
   2. P′ = (6, −2), so the x-coordinate is 6.

   Answer: 6

3. Example 3

   Triangle ABC is congruent to triangle DEF. AB = 19 cm, BC = 12 cm, and CA = 15 cm. What is the length of EF, in cm?

   1. Congruent figures have equal corresponding sides. Match the letters in order: A↔D, B↔E, C↔F.
   2. EF corresponds to BC, so EF = 12 cm.

   Answer: 12