Matching the Corners
Part of the Triangles section of Coddy's Geometry journey. Lesson 47 of 63.
You do not need a statement like △ABC ~ △DEF to know two triangles are similar. Two pairs of equal angles are enough. If two angles match, the third angles match as well, since each is 180 minus the other two. This is AA similarity.
Then match the corners by the marks, not by how the triangles are drawn. Here one arc sits at A and at P, two arcs at B and at Q. So A matches P, B matches Q, C matches R, and △ABC ~ △PQR even though PQR is turned over. Side AB matches PQ.
One pair of equal angles is not enough: the other two angles could share what is left in many ways.
Challenge
The arcs mark two pairs of equal angles in △ABC and △PQR. Is there enough to find PQ? Answer, and if it is, find PQ. Press Check after each.
Try it yourself
Is there enough information?
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 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 Leg9Similar Triangles
Same Shape, Different SizeThe Scale FactorFinding a SideMatching the CornersRecap: Similar Triangles