10th grade math worksheets
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Triangle congruence rules
Grade 8–10
Name the congruence rule (SSS, SAS, ASA, AAS, HL) from the marks on a pair of triangles
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What to practice this year
A two-column proof is the year’s real work, and it comes in two sizes. Naming which criterion applies — SSS, SAS, ASA, AAS or HL — is a reading of the marks on a figure. Writing the proof that uses it is a different act, and the sheets separate them: one set blanks a single reason, the other hands over an empty Statements and Reasons table with nothing but the Given and the Prove. Every answer key sets the model proof out in full, line by line.
Why these skills come next
Circles carry the year’s densest set of named results — the inscribed angle and its central twin, arc length and sector area, and the two circles a triangle defines.
Nothing matches that. Try a skill, a number, or a topic.
Step 1 of 14
Congruence and similarity
Name the criterion from the marks on a figure — SSS, SAS, ASA, AAS or HL.
Step 2 of 14
Symmetry as a motion
Which turns carry a shape back onto itself — the half of symmetry that is not a fold.
Step 3 of 14
Modeling with geometry
A figure with a quantity on it: work out the size, then how much sits in one unit of it.
Step 4 of 14
Probability rules
“And” is one cell of a two-way table; “or” is three, minus the one counted twice.- The addition rule
Print Bus OR Late → 65% - Independent events
Print 40% × 60% = 24%, table 14% - Arranging things in order
Print 5 books on a shelf → 120 - Permutations
Print 7 runners, 3 medals → 210 - Combinations
Print 3 of 7 students → 35 - Permutations and combinations
Print 7 runners, 3 medals → 210 - Correlation and causation
Print more police, more crime → second causes first - Survey, experiment or study?
Print randomly given the drug → experiment - Is this sample fair?
Print only the soccer team is asked → a group is left out - Does the data fit the claim?
Print 1 in 5 of 200 is 40; the result was 84 - Margin of error
Print 400 asked → 5%
Step 5 of 14
Compass constructions
The seven straightedge-and-compass constructions, in the order each is built out of the one before it.
Step 6 of 14
Two-column proofs
Fill the missing reason, then write the whole argument from an empty table.- Triangle congruence proofs
Print AC ≅ AC → ? - Similar triangle proofs
Print DE ∥ BC → ? - CPCTC proofs
Print △ABC ≅ △ADC → ∠B ≅ ∠D - Parallelogram proofs
Print ABCD is a parallelogram → AB ≅ CD - Write a triangle proof
Print Given → Prove - Write a similarity proof
Print Given -> Prove - Altitude to the hypotenuse
Print p 4, q 9 → h
Step 7 of 14
Circles
Inscribed angles, arc length and sector area, and a triangle's two circles.- Inscribed angle in a circle
Print center 120° → circle __° - Find the inscribed angle
Print center 130° → circle __° - Find the central angle
Print circle 65° → center __° - Arc length and sector area
Print r = 10, 90° slice - Circumscribed circle of a triangle
Print 15, 20, 25 → R = __ - Inscribed circle of a triangle
Print 15, 20, 25 → r = __
Step 8 of 14
Right-triangle trigonometry
Write a ratio as a fraction, then use it to find a missing side or angle.
Step 9 of 14
Coordinate geometry
When two lines are parallel or perpendicular, and what a circle's equation hides.- Parallel and perpendicular lines
Print (3, 15), x + 4y = 4 - Perimeter from coordinates
Print (1, 1), (9, 1), (5, 4) - Area from coordinates
Print (4, 4), (6, 4), (6, 1) - Equation of a parallel line
Print (−2, −7), y = 4x + 4 - Equation of a perpendicular line
Print (−1, 2), x + 4y = 8 - The equation of a circle in standard form
Print (x − 1)² + (y + 6)² = 4 - The equation of a circle
Print x² + y² − 6x − 12y + 29 = 0 - The equation of a parabola
Print focus (2, −5), y = 3
Step 10 of 14
Radicals and rational exponents
Simplify a root, then write it as a power instead.
Step 11 of 14
Completing the square
Rewrite a quadratic as a square plus a number — the move that solves any of them.
Step 12 of 14
Complex numbers
When the discriminant is negative, and the arithmetic of a ± bi.- Quadratics with complex solutions
Print x² − 6x + 45 = 0 - Quadratics with complex conjugate roots
Print x² − 4x + 68 = 0 - Complex numbers
Print (3 + 2i)(1 − 4i) - Adding and subtracting complex numbers
Print (6 − 3i) + (5 − 6i) - Powers of i
Print i¹⁷ = i - Multiplying complex numbers
Print (2 − 2i)(4 + 2i) - Dividing complex numbers
Print (−2 + 3i) ÷ (2 + 3i)
Step 13 of 14
Rearranging formulas
Make any letter the subject — thirty formulas a course uses, and ax + by = c.
Step 14 of 14
