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Geometry Proofs - CPCTC, Two-Column Proofs, FlowChart Proofs and Proof by Contradiction

Videos, worksheets, games and activities to help Geometry students learn geometry proofs and how to use CPCTC, Two-Column Proofs, FlowChart Proofs and Proof by Contradiction.

Related Topics:
More Grade 9 and Grade 10 math


CPCTC is an acronym for corresponding parts of congruent triangles are congruent. CPCTC is commonly used at or near the end of a proof which asks the student to show that two angles or two sides are congruent. It means that once two triangles are proven to be congruent, then the three pairs of sides that correspond must be congruent and the three pairs of angles that correspond must be congruent.

How to use the principle that corresponding parts of congruent triangles are congruent, or CPCTC.
This video offers a look at two triangle proofs that involve the CPCTC theorem.
How do we use CPCTC?

Two Column Proofs

Two column proofs are organized into statement and reason columns. Each statement must be justified in the reason column. Before beginning a two column proof, start by working backwards from the "prove" or "show" statement. The reason column will typically include "given", vocabulary definitions, conjectures, and theorems.

How to organize a two column proof.

This video introduces the structure of 2 column proofs and works through three examples.
A brief lesson and practice on drawing diagrams and completing two column proofs from word problems.
Example 1: Two circle intersect at two points. Prove that the segment joining the centers of the circles bisects the segment joining the points of intersection.
Example 2: If each pair of opposite sides of a four sided figure are congruent, then the segments joining opposite vertices bisect each other.
Example 3: If a point on the base of an isosceles triangle is equidistant from the midpointd od the legs, then that pint ids the midpoint of the base.


Flowchart Proofs

Flowchart proofs are organized with boxes and arrows; each "statement" is inside the box and each "reason" is underneath each box. Each statement in a proof allows another subsequent statement to be made. In flowchart proofs, this progression is shown through arrows. Flowchart proofs are useful because it allows the reader to see how each statement leads to the conclusion.

How to outline a flowchart proof. Using flow charts to do proofs.
Using flowcharts in proofs for Geometry.

Proof by Contradiction

CA Geometry: Proof by Contradiction
CA Geometry: More Proofs


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