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    • ▾High school geometry
      • ▸Basics of geometry
        • •Proofs in this course
        • •Geometric definitions
        • •Linear pair theorem
        • •Area of a regular polygon
        • •Diagonal length of a right rectangular prism
        • •Distance and midpoint in 3D
        • •Circumcircles and incircles
      • ▸Transformations
        • •Preserved properties of rigid transformations
        • •Find measures using rigid transformations
        • •Find the angle of rotation
        • •Find the sequence of rigid transformations
        • •Reflecting figures
        • •Reflecting a point over any non-horizontal line
      • ▾Congruence
        • •Congruent polygons
        • •Congruent supplements and complements theorems
        • •ASA and AAS congruence
        • •Isosceles triangle theorem and its converse
        • •SSS congruence
        • •SAS congruence
        • •Converse of the Pythagorean theorem
        • •Proving isosceles trapezoids
      • ▸Similarity
        • •Intro to similarity
        • •All circles are similar
        • •Finding angles and side lengths in similar polygons
        • •Finding the scale factor for similar polygons
        • •Third angle theorem
        • •Similar triangles
        • •Ratios of area, surface area, and volume, for similar shapes
        • •Crossed ladders theorem
      • ▸Polygons
        • •Perimeter of composite figures
        • •Finding the volume and surface area of composite figures
        • •Sum of the interior angles of a triangle
        • •Sum of interior angles for simple polygons
        • •Sum of exterior angles
        • •Pentagonal tilings
      • ▸Incenter and circumcenter of a triangle
        • •Intro to the incenter and circumcenter of a triangle
        • •Perpendicular bisector theorem and its converse
        • •Circumcenter theorem
        • •Angle bisector theorem
        • •Incenter theorem
      • ▸Triangles
        • •Euler line
        • •Geometric mean theorems
        • •AM-GM inequality
        • •Triangle angle bisector theorem
        • •Ceva's theorem
        • •Proving the altitude of an isosceles triangle cuts two congruent right triangles
        • •Centroid and orthocenter
        • •Ordering triangle sides and angles
        • •Midsegment and proportionality theorems
        • •Menelaus's theorem
        • •Side splitter theorem
        • •Hinge theorem and its converse
        • •Hypotenuse-leg congruence theorem
        • •Hypotenuse-angle congruence theorem
        • •Areas of triangles and quadrilaterals on grids
        • •Exterior angle theorem
      • ▸Quadrilaterals
        • •Diagonals of a kite are perpendicular
        • •Diagonals of a parallelogram bisect each other
        • •Diagonals of a rhombus are perpendicular bisectors
        • •Area of a rhombus from diagonals
        • •Diagonals of a rectangle are congruent
        • •Opposite sides of a parallelogram are congruent
        • •Opposite angles of a parallelogram are congruent
        • •British flag theorem
        • •Cyclic quadrilaterals
        • •Fuhrmann's theorem
        • •Classifying quadrilaterals from four points
      • ▸Circle theorems
        • •Thales's theorem and its converse
        • •Central angle theorem
        • •Angles standing on the same arc are congruent
        • •Chord properties
        • •Congruent tangents theorem
        • •Radius and tangent theorem
        • •Radii inside right triangles
        • •Alternate segments theorem
        • •Power of a point
        • •Three squares puzzle
      • ▸Volume and surface area
        • •Cavalieri's principle
        • •Volume of prisms and cylinders
        • •Volume and surface area of a sphere
      • ▸Analytic geometry
        • •A square within a square
     › High school geometry › Congruence

    SSS congruence

    Students will learn what the SSS congruence theorem says, and see a proof using rigid transformations.

    Proving the SSS triangle congruence criterion using transformations by Khan Academy

    Students should also learn how Euclid proved the SSS congruence theorem. His proof can be seen by reading this, then this.

    After that, students will learn how to use the SSS theorem.

    Watch these Brian McLogan videos:

    • How to Write a Proof Using SSS Congruence Theorem
    • Writing a Proof for Two Triangles Congruent Under SSS

    There might be more videos on using the SSS congruence theorem here.

    Conclude by giving your students these challenges:

    • Doughnut Percents by NRICH
    • Making Shapes by NRICH
    • Pocket Money by NRICH
    • 2014 AMC 8, Problem 24
    • 2004 AMC 8, Problem 2