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Three Sides Fix It

Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 11 of 63.

Give someone three sticks and ask for a triangle. However they lay them, the triangle comes out the same: they can turn it or flip it, but the corners cannot change. Three lengths leave the triangle no room to move.

$Sides 5 and 5 on a base of 6 reach the same height above and below the base$

Here sides of 5 and 5 on a base of 6 meet at C, or at D below the base. The two triangles are mirror images, so one flipped over fits the other: they are congruent. That is why three pairs of equal sides are enough to prove two triangles congruent.

Challenge

Side AB is 4. Drag the corner C until AC is 5 and BC is 3. The board shows each length as you drag. Then press Check.

Try it yourself

$Drag the figure and watch$

Drag the figure and watch

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Congruence & Proof

2Congruent Triangles

Same Size, Same Shape Matching Sides Matching Angles What Congruence Gives Recap: Matching Parts

5ASA and AAS

The Side Between The ASA Rule The AAS Rule ASA or AAS?Recap: ASA and AAS

8Proofs with Vertical Angles

Vertical Angles in Proofs The Bowtie Bowtie with ASA Linear Pairs in Proofs Recap: Vertical Angles

11Similarity Proofs

AA Similarity Two Right Triangles SSS Similarity SAS Similarity Similar, Then Find Recap: Similarity

3SSS

Three Sides Fix ItThe SSS Rule A Shared Side SSS with a Shared Side Recap: SSS

6HL for Right Triangles

Hypotenuse and Legs The HL Rule Why HL Works HL with a Shared Leg Recap: HL

9Proofs with Parallel Lines

Parallel Angles as Reasons Alternate Angles in a Proof Corresponding Angles in Proofs Parallel or Not?Recap: Parallel Proofs

12Final Challenges

Final: The Kite Diagonals Final: Overlapping Triangles Final: Enough to Find It?Final: The Height Bisects Final: The Roof Frame