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More Geometry Lessons

Videos, examples, solutions, worksheets, games and activities to help Geometry students learn how to use two column proofs.

A two-column proof consists of a list of statements, and the reasons why those statements are true. The statements are in the left column and the reasons are in the right column. The statements consists of steps toward solving the problem.

The following figure gives a Two-column Proof for the Isosceles Triangle Theorem. Scroll down the page for more examples and solutions.

**Two-Column Proof (5 steps) Practice 1**

Practice writing a 2 column proof.

Example:

Given AD = 8, BC = 8, B̅C̅ ≅ C̅D̅

Prove: A̅D̅ ≅ C̅D̅**Two-Column Proof (7 steps) Practice 2**

Practice writing two column proofs.

Example:

Given D̅E̅ ≅ F̅G̅

Prove: x = 4

**Proof Practice (5 steps) Practice 3**

Practice writing two column proofs.

Example:

Given MN = PQ

Prove: MP = NQ**Practice Proof 4 (Use angle addition postulate)**

Practice writing 2 column proofs.

Example:

Given m∠RPS = m∠TPC, m∠TPV = m∠SPT

Prove: m∠RPV = 3(m∠RPS)**How to use the two-column proof to prove the Isosceles Triangle Theorem?**

The Isosceles Triangle Theorem states that if two sides of a triangle are congruent, then the angles opposite the sides are congruent.

**How to use the two-column proof to prove the Exterior Angle Theorem?**

The Isosceles Triangle Theorem states that the sum of the remote interior angles is equal to the non-adjacent exterior angle.

**How to use two column proof to show segments are perpendicular?**

Use the SSS, SAS, ASA, AAS postulates.

Using triangle congruency postulates to show that two intersecting segments are perpendicular. (Diagonals of a kite)

**How to use two column proof to prove parallel lines?**

Given ∠2 ≅ ∠1 ≅ ∠3

Prove: A̅B̅ || C̅D̅

**Proving a Quadrilateral is a Parallelogram | Geometry Proof**

This video geometry lesson proves two parallelogram theorems using the two column proof.

Proof 1: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Proof 2: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Theorems Used: If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram and If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram to solve problems.**Special Parallelograms - Rhombus and Rectangle Proofs**

This video uses the two column method to prove two theorems.

Proof 1: The diagonals of a rectangle are congruent. This amounts to be a triangle proof to use CPCTC.

Proof 2: The diagonals of a rhombus are perpendicular.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Geometry Lessons

A two-column proof consists of a list of statements, and the reasons why those statements are true. The statements are in the left column and the reasons are in the right column. The statements consists of steps toward solving the problem.

The following figure gives a Two-column Proof for the Isosceles Triangle Theorem. Scroll down the page for more examples and solutions.

Practice writing a 2 column proof.

Example:

Given AD = 8, BC = 8, B̅C̅ ≅ C̅D̅

Prove: A̅D̅ ≅ C̅D̅

Practice writing two column proofs.

Example:

Given D̅E̅ ≅ F̅G̅

Prove: x = 4

Practice writing two column proofs.

Example:

Given MN = PQ

Prove: MP = NQ

Practice writing 2 column proofs.

Example:

Given m∠RPS = m∠TPC, m∠TPV = m∠SPT

Prove: m∠RPV = 3(m∠RPS)

The Isosceles Triangle Theorem states that if two sides of a triangle are congruent, then the angles opposite the sides are congruent.

The Isosceles Triangle Theorem states that the sum of the remote interior angles is equal to the non-adjacent exterior angle.

Use the SSS, SAS, ASA, AAS postulates.

Using triangle congruency postulates to show that two intersecting segments are perpendicular. (Diagonals of a kite)

Given ∠2 ≅ ∠1 ≅ ∠3

Prove: A̅B̅ || C̅D̅

This video geometry lesson proves two parallelogram theorems using the two column proof.

Proof 1: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Proof 2: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Theorems Used: If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram and If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram to solve problems.

This video uses the two column method to prove two theorems.

Proof 1: The diagonals of a rectangle are congruent. This amounts to be a triangle proof to use CPCTC.

Proof 2: The diagonals of a rhombus are perpendicular.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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