I really need some help please!!!!!
Am I on the right tract?
Given: ABCD is a parallelogram; <1 is congruent to <2
To Prove: ABCD is a Rhombus
Plan: Show <2 is congruent to < CAB.
hence CB is congruent to AB,
making ABCD a parallelogram
with consecutive sides congruent
PROOF
Statements Reasons
1. ABCD is a parallelogram 1.Given
<1 is congruent to <2
2. Draw segment from A to C 2. Two points determine exactly one line
3.< 1 & <3 are congruent 3. Alternate angles are congruent
4. AC bisects angle 1&2 4. Def. of Angle bisector
5 . m<DAB=m<BCD 5. Opposite angles in a parallelogram are equal
6. <2 & <3 are congruen6.Transitiveprop 7 .AB=BC 7. Sides oposite are
congruent angles
8.<1&<2 8. Cor.parts are equal
9.AB=BC=CD=DA 9. ABCD is a rhombus
I cant follow it without a diagram, sorry.
I sorry but I don't know how to use the computer to draw.
No problem! I can still help you understand the proof without a diagram. Let's break down the steps.
Given:
1. ABCD is a parallelogram.
2. <1 is congruent to <2.
To Prove:
ABCD is a rhombus.
Plan:
1. Show <2 is congruent to <CAB.
2. This implies that CB is congruent to AB.
3. Conclude that ABCD is a parallelogram with consecutive sides congruent.
Proof:
Statements Reasons
1. ABCD is a parallelogram Given
2. <1 is congruent to <2 Given
3. Draw segment from A to C Two points determine exactly one line
4. <1 and <3 are congruent Alternate angles are congruent
5. AC bisects angle 1 and 2 Definition of Angle bisector
6. m<DAB = m<BCD Opposite angles in a parallelogram are equal
7. <2 and <3 are congruent Transitive property
8. AB = BC Sides opposite to congruent angles are congruent
9. <1 and <2 Corresponding parts of congruent angles are equal
10. AB = BC = CD = DA Consecutive sides of a parallelogram are congruent, making ABCD a rhombus
I hope this helps clarify the steps of the proof for you!