Similar Triangles Homework

Homework 2: Similar Figures

Congruent Angles and Proportions of Corresponding Sides

• Triangles FGH and JKH
  • Angles: $\\angle F \\cong \\angle J$, $\\\angle G \\cong \\angle K$, $\\\angle H \\cong \\angle H$
  • Sides: $\frac{FG}{JK} = \frac{GH}{KH} = \frac{FH}{JH}$

Scale Factor of Similar Polygons

• Sides of A: 4 and 2, Sides of B: 16 and 8
  • Scale Factor: $\frac{4}{16} = \frac{2}{8} = \frac{1}{4}$ or 1:4

Using Scale Factor to Find Unknown Values

• Scale factor of Figure A to Figure B is 4:5, find x (sides 10 and x)
  • A/B = 4/5: $\frac{10}{x} = \frac{4}{5}$, $4x = 50$, $x = 12.5$
• Scale factor of Figure A to Figure B is 7:2, find the perimeter of Figure A (sides 21 and 28).
  • Perimeter of Figure A: $21 + 28 = 49$

Similar Triangles

• If ABC \~ DEC, find x and y. $\frac{AB}{DE} = \frac{BC}{EC} = \frac{AC}{DC}$
• If JKL \~ NMP, find x. $\frac{JK}{NM} = \frac{JL}{NP}$
• If DGH \~ DEF, find x. $\frac{DG}{DE} = \frac{GH}{EF}$
• If XYZ \~ RST, find RS. $\frac{XY}{RS} = \frac{YZ}{ST}$
• If ABC \~ EDC, find AC. $\frac{AB}{ED} = \frac{BC}{EC} = \frac{AC}{DC}$
• If JKL \~ MKN, find x. $\frac{JK}{MK} = \frac{KL}{KN}$
• If BCD \~ GEF, find BD. \frac{BC}{GE} = \frac{CD}{EF}

1. Congruent Angles and Proportions of Corresponding Sides

   • Explain that similar figures have congruent angles and proportional corresponding sides.
   • Example: Triangles FGH and JKH. List the congruent angles and the side proportions.

2. Scale Factor of Similar Polygons

   • Define scale factor as the ratio of corresponding side lengths.
   • Explain how to calculate it (e.g., \frac{Side of A}{Side of B}$$).
   • Example: Sides of polygons A and B with the calculation