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Same Size, Same Shape

Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 5 of 60.

Two shapes are congruent when one fits exactly on top of the other. We write ≅. To make it fit, you may slide it, turn it or flip it over. You may not stretch it. Looking alike is not enough. It must fit exactly.

When it fits, list the corners in the order they land. △ABC ≅ △DEF means A lands on D, B lands on E and C lands on F. The first letter goes with the first, the second with the second, and the third with the third.

Triangles ABC and DEF, the second a flipped copy of the first, with matching tick marks on matching sides

challenge icon

Challenge

Move △ABC so it lands exactly on the dashed triangle. Choose a move (slide, turn or flip), set it up and apply it. Then press Check.

Try it yourself

Move the shape onto its target

Move the shape onto its target

All lessons in Congruence & Proof

1What a Proof Is

Given and ProveChaining Equal PartsYour First Full ProofRecap: A Chain of Reasons

4SAS

The Included AngleThe SAS RuleSAS with a Shared SideWhy SSA FailsSAS or SSS?Recap: SAS

7Using CPCTC

Congruent, Then EqualProving a BisectorFlowchart ProofsProving a MidpointRecap: Using CPCTC

10Isosceles Triangle Proofs

Base Angles in a ProofEqual Angles, Equal SidesProving IsoscelesThe Perpendicular BisectorChasing in Isosceles ShapesRecap: Isosceles Proofs

2Congruent Triangles

Same Size, Same ShapeWhat Congruence GivesRecap: Matching Parts

5ASA and AAS

The Side BetweenThe ASA RuleThe AAS RuleASA or AAS?Recap: ASA and AAS

8Proofs with Vertical Angles

Vertical Angles in ProofsThe BowtieBowtie with ASALinear Pairs in ProofsRecap: Vertical Angles

11Similarity Proofs

AA SimilarityTwo Right TrianglesSSS SimilaritySAS SimilaritySimilar, Then FindRecap: Similarity

3SSS

Three Sides Fix ItThe SSS RuleA Shared SideSSS with a Shared SideRecap: SSS

6HL for Right Triangles

Hypotenuse and LegsThe HL RuleWhy HL WorksHL with a Shared LegRecap: HL

9Proofs with Parallel Lines

Parallel Angles as ReasonsAlternate Angles in a ProofCorresponding Angles in ProofsParallel or Not?Recap: Parallel Proofs

12Final Challenges

Final: The Kite DiagonalsFinal: Overlapping TrianglesFinal: Enough to Find It?Final: The Height BisectsFinal: The Roof Frame