Transitive Property of Equality Variation 2
Angle Symmetry Example 2
Distance Property 2
Distance Property 1
Collinear Then 180
Subtract Both Sides
Add Term to Both Sides 6
Subtract Both Sides 2
Add Term to Both Sides 7
Transitive Property of Equality Variation 1
Vertical Angles
Angle Addition Theorem
Collinear Angles Property 9
Collinear Angles B
Exterior Angle
Exterior Angle B
Collinear Angles Property 10
Collinear Angles Property 3
Collinear Angles Property 3 B
Collinear Angles Property 3 C
alternate interior angles then parallel
ParallelThenAIA
Parallelthenaiashort
Parallel Then Aia Short Mirror
Angle Symmetry 4
Angle Symmetry Example
If Parallelogram Diagonal Then Congruent Triangles
If Parallelogram Then Sides Congruent B
If Parallelogram Then Sides Congruent B2
Square is Equilateral
If Parallelogram Then Sides Congruent
Transitive Property of Equality Variation 3
Distance Property 5
Square is Equilateral 2
Square is Equilateral 3
Distance Property 6
Congruent Triangles to Angles
Aiathenparallelshort
Congruent Triangles to Angles 2
Parallel Then Parallelogram
If Sides Congruent Then Parallelogram
If Sides Congruent Then Parallelogram 2
If Sides Congruent Then Parallelogram 3
If Equilateral Then Rhombus
Square is Rhombus
Parallel Then Aia Short Mirror 3
Equal Angles
Angle Symmetry 2
Angle Symmetry 3
Parallel Then Aia Short 3
Angle Symmetry Property 5
Triangles Inside Rhombus
Sides of Rhombus Congruent 4
Equal Angles 2
Diagonal Bisects Rhombus 2
Parallel Then Aia 2
Converse of the Supplementary Angles Theorem
Commutative Property Example 2
Commutative Property Variation 1
Substitution 2
Substitution 8
Substitution Example 10
Supplementary Then 180
Parallel Then Interior Supplementary
Paralleltheninteriorshort
Subtraction Example 2
Add Number to Both Sides
Add Number to Both Sides 2
Rectangle Right Angles 2
Angle Addition Theorem 2
Substitute 2
Multiplicative Identity 2
Distributive Property 4
Multiplicative Property of Equality Variation 1
Addition Theorem
Double
Divide Both Sides
Multiplicative Property of Equality Variation 2
Division is Commutative
Associative Property
Divide Each Side
Reduce Addition 2
Square Example 2

Proof: Square Example 2

Let's prove the following theorem:

if ABCD is a square, then m∠BCA = 45

A B C D

Proof:

View as a tree | View dependent proofs | Try proving it

Given
1 ABCD is a square
Proof Table
# Claim Reason
1 ABCD is a rhombus if ABCD is a square, then ABCD is a rhombus
2 m∠BCA = m∠DCA if ABCD is a rhombus, then m∠BCA = m∠DCA
3 m∠BCA = m∠ACD if m∠BCA = m∠DCA, then m∠BCA = m∠ACD
4 ABCD is a rectangle if ABCD is a square, then ABCD is a rectangle
5 BCD is a right angle if ABCD is a rectangle, then ∠BCD is a right angle
6 m∠BCD = 90 if ∠BCD is a right angle, then m∠BCD = 90
7 quadrilateral ABCD is convex if ABCD is a rectangle, then quadrilateral ABCD is convex
8 point A lies in interior of ∠BCD if quadrilateral ABCD is convex, then point A lies in interior of ∠BCD
9 (m∠BCA) + (m∠ACD) = m∠BCD if point A lies in interior of ∠BCD, then (m∠BCA) + (m∠ACD) = m∠BCD
10 (m∠BCA) + (m∠BCA) = m∠BCD if (m∠BCA) + (m∠ACD) = m∠BCD and m∠BCA = m∠ACD, then (m∠BCA) + (m∠BCA) = m∠BCD
11 (m∠BCA) + (m∠BCA) = 90 if (m∠BCA) + (m∠BCA) = m∠BCD and m∠BCD = 90, then (m∠BCA) + (m∠BCA) = 90
12 m∠BCA = 45 if (m∠BCA) + (m∠BCA) = 90, then m∠BCA = 45
Previous Lesson

Comments

Please log in to add comments