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Final: The Kite Diagonals

Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 56 of 60.

Kite PQRS has PQ = PS and RQ = RS, as the ticks show. Its diagonals PR and QS cross at O.

Prove that the diagonal PR cuts QS in half: O is the midpoint of QS.

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Challenge

In kite PQRS the ticks show PQ = PS and RQ = RS, and the diagonals cross at O. Prove that O is the midpoint of QS, then press Check.

Try it yourself

Write the proof

Write the proof

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