Proof for Theorem
Prove: If a parallelogram is a rhombus, its diagonals are perpendicular.
thrhombus3given
thrhombus1
 
Statements
  
Reasons
1.
rhombus ABCD
1.
Given
2.
pf1
2.
A rhombus is a parallelogram with 4 congruent sides.
3.
thrhombus13
3.
A rhombus is a parallelogram with 4 congruent sides.
4.
thrhombus34
4.
Diagonals of a parallelogram bisect each other.
5.
3Rtris
5.
SSS - if 3 sides of one Δ are congruentto the corres. parts of another Δ, the Δs are congruent.
6.
thrhombus36
6.
CPCTC - corres. parts of congruentΔs are congruent.
7.
3R7
7.
congruent∠s are ∠s of = measure.
8.

3R8
8.
The sum of the ∠s surrounding a point, sharing a vertex, is 360º.
9.
thrhombus39
9.
Substitution
10.
thrhombus310
10.
Combine like terms.
11.
thrhombus311
11.
Division
12.
∠AED right angle
12.
A right ∠ is an ∠ of 90º.
13.
thrhombus313
13.
Perpendicular lines meet to form right angles.

All Rights Reserved - Copyright MathBitsNotebook.com