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    • ▾8th grade
      • ▸Numbers and operations
        • •Irrational numbers
        • •Evaluating square roots of small perfect squares
        • •Approximating square roots
        • •Evaluating cube roots of small perfect cubes
        • •Negative bases
        • •Negative exponents
        • •Approximating with powers of 10
        • •Proving properties of even, odd, and square numbers
        • •Divisibility with sums and differences
        • •Proving the divisibility rules for 7 and 13
        • •1089 trick
      • ▸Properties of exponents
        • •Power of a power rule for exponents
        • •Power of a product rule for exponents
        • •Power of a quotient rule for exponents
        • •Product of powers rule for exponents
        • •Quotient of powers rule for exponents
        • •Multi-step problems, properties of exponents
        • •Simplifying square roots of decimals and fractions
      • ▸Scientific notation
        • •Intro to scientific notation
        • •Converting between scientific notation and standard form
        • •Comparing numbers in scientific notation
        • •Adding and subtracting in scientific notation
        • •Multiplying and dividing in scientific notation
        • •Scientific notation, multi-step word problems
      • ▸Linear functions and equations
        • •Mentally solving certain multi-step equations
        • •Number of solutions to linear equations
        • •Finding the equation of a line
        • •Graphing proportional relationships
        • •Analyzing graphs of step functions
        • •Intro to functions
        • •Slope-intercept form
        • •Slope-intercept form from word problems
        • •Understanding slope with similar triangles
        • •Solving multi-step equations
      • ▸Linear systems of equations in two variables
        • •Testing solutions to linear systems of equations in two variables
        • •Solving linear systems of equations in two variables by graphing
        • •Solving linear systems of equations in two variables by substitution
        • •Solving linear systems of equations in two variables by elimination
        • •Number of solutions to a system of equations algebraically
        • •Solving linear systems of equations in two variables by any method
        • •Age problems
      • ▾Geometry
        • •Deriving the surface area and volume formulas for spheres
        • •Changing linear dimensions
        • •Congruent figures
        • •Corresponding angle theorems
        • •Converse of the corresponding angle theorems
        • •Proving lines are parallel
        • •Pythagorean theorem
        • •Missing square puzzle
        • •Finding the diagonal length of a rectangle
        • •Pythagorean triples
        • •Proving the inverse Pythagorean theorem
        • •Pythagorean inequality theorem
        • •Distance formula
        • •Volume
        • •Midpoint formula
        • •Symmetry
      • ▸Geometric transformations
        • •Dilating lines
        • •Dilating polygons
        • •Scaling along an axis
        • •Reflecting across axes
        • •Rigid transformations
      • ▸Data and modeling
        • •Estimating the line of best fit
        • •Making and describing scatter plots
     › 8th grade › Geometry

    Corresponding angle theorems

    Students will begin by learning what the corresponding angles postulate is (video). Then students will learn what the other three corresponding angle theorems are, and see a proof of each. These include the consecutive interior angles theorem, the alternate interior angles theorem, and the alternate exterior angles theorem. Then students will practice using these theorems. Some problems will require students to determine a missing angle, or angles (video), while others will require solving a linear equation (video). Here's an easy problem: Prove adjacent interior angles in a parallelogram are supplementary. This is a direct consequence of the consecutive interior angles theorem. Here's a video detailing the proof. The fact that adjacent interior angles are supplementary in parallelograms, will be used later to prove the converse of Thales's theorem.

    Next, give your students these challenges:

    • Andy's Marbles by NRICH

    How many squares are in this picture?

    Here's the answer: There are 9 1x1 squares, 4 2x2 squares, and 1 3x3 square. Thus, there are 14 squares in total.

    Conclude by leading this investigation:

    ConHex (strategy game)
    by MathPickle

    Lessons and practice problems