Final: Three Sticks
Part of the Triangles section of Coddy's Geometry journey. Lesson 67 of 71.
The triangle inequality says that the third side of a triangle must be longer than the difference of the other two sides and shorter than their sum. Take known sides 8 and 5. The difference is 3 and the sum is 13, so the third side x satisfies 3 < x < 13. Write both bounds as one chain inequality, then work out the difference and the sum. The ends are not included, because with a third side of 3 or 13 the three sides would lie flat in a line.
Challenge
Two sides of a triangle are 20 and 13.
Find the range of the third side x.
Try it yourself
Solve for x
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Triangles
1Sides and Names
Three Sides, Three CornersSorting by SidesNaming by AnglesTicks into EquationsThe Longest SideRecap: Sorting Triangles2The Triangle Inequality
Can Three Sticks Meet?Exactly ReachingHow Short Can It Be?How Long Can It Be?The Range of the Third SideThe FormulaWhole-Number SidesRecap: The Third Side5The Hypotenuse
Squares on the SidesFinding the HypotenusePythagorean TriplesWhen It Is Not WholeSimplifying the RootRecap: The Hypotenuse8Special Right Triangles
The 45-45-90 TriangleLegs from the HypotenuseThe 30-60-90 TriangleAll Three SidesWhich Triangle Is It?Recap: Special Triangles11Mixing Area and Pythagoras
Height of an IsoscelesArea from the HeightThe Equilateral TriangleRight Triangle PerimeterRecap: Two Tools3Perimeter
Around the EdgeA Missing SideIsosceles PerimeterEquilateral PerimeterSides as ExpressionsWrite the PerimeterRecap: Around the Edge6Finding a Leg
Working BackwardsThe LadderWhich Side Is c?A Leg That Is Not WholeRecap: Finding a Leg9Similar Triangles
Same Shape, Different SizeThe Scale FactorFinding a SideThe Unknown BelowMatching the CornersRecap: Similar Triangles12Final Challenges
Final: Three SticksFinal: The FenceFinal: The LadderFinal: The ShadowFinal: Master of Triangles