A Side with an Expression
Part of the Triangles section of Coddy's Geometry journey. Lesson 52 of 63.
When a side is written with a letter, the proportion becomes an equation. Pair the sides by the matching corners, write the two ratios equal, and solve.
The arcs give ∠A = ∠D and ∠B = ∠E, so △ABC ~ △DEF. AB matches DE and CA matches FD: 4/(x + 2) = 3/6. The right side is 1/2, so x + 2 = 8 and x = 6. Check: DE = 8 is twice AB, like FD is twice CA.
On the board, tap the four sides, pick Similar triangles, and the board writes the proportion. Then clear the fractions with the moves.
Challenge
The arcs show △ABC ~ △DEF. Tap the sides you need, pick the rule, and solve the equation the board writes for x.
Then press Check.
Try it yourself
Use the figure to find 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 Triangles4Area of a Triangle
Half the RectangleHeight Is Not a SideRight Triangle AreaFinding the HeightAny Side Can Be the BaseRecap: Area10Scale in the World
ShadowsAcross the RiverNested TrianglesA Side with an ExpressionRecap: Scale in the World2The Triangle Inequality
Can Three Sticks Meet?Exactly ReachingThe Range of the Third SideThe FormulaRecap: The Third Side5The Pythagorean Theorem
Squares on the SidesFinding the HypotenusePythagorean TriplesWhen It Is Not WholeRecap: The Hypotenuse3Perimeter
Around the EdgeA Missing SideIsosceles PerimeterSides as ExpressionsRecap: Around the Edge6Finding a Leg
Working BackwardsThe LadderWhich Side Is c?A Leg That Is Not WholeRecap: Finding a Leg