12.1 Right Triangles and Quadrilaterals

Links and useful resources

• gr7's Prealgebra Course Outline START HERE<<<
• AoPS Online Textbook
• IXL Grade 7 index
• IXL Grade 8 index
• AoPS Alcumus
• IXL prealgebra practice index
• OpenSTAX Prealgebra-1 textbook

Concept summary and lesson

• The pythagorean theorem

  • $a^2+b^2=c^2$ , where $a,b,c$ are the lengths of the sides of a right triangle

• Find a missing side length for a right triangle

  • if $a=12$ and $c=13$, what is $b$?
  • if $a=2$ and $b=2$, what is $c$?
  • if $c=2a$, what is $b$?

• hypotenuse and legs of right triangle

  • The hypotenuse is always longer than either leg, but shorter than the sum of the legs. Why?

• Can a right triangle be isosceles? Equilateral? Obtuse? Acute?

  • draw pictures. Check in with the pythagorean theorem, use logic.

• Rectilinear paths and displacement.

  • If I follow a path that goes north 5, then east 2, then north 10, then west 3, how for north and east am I from where I started?
  • What is my distance from where I started?

Guided practice

• Set up the problem above by labeling all of the parts of the diagram with either numbers or variable names, and writing down any equations that you think will help.
• Use the two-column format to solve the problem.

Homework

• #hw (math) (gr7) Read section 12.1 The Pythagorean Theorem (p. 442) and do problems 2025-03-20