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 congruent 6. Transitive prop 7 . AB=BC 7. Sides oposite are congruent angles
8.<1 & <2 8. Cor.parts are eual
9. AB=BC=CD=DA 9. ABCD is a rhombus
10. Therefore, ABCD is a rhombus
Reason: When all four sides of a parallelogram are congruent, it is a rhombus. And in this case, we have shown that AB = BC = CD = DA.
Proof:
1. Given: ABCD is a parallelogram and <1 is congruent to <2
Reason: Given information
2. Draw a segment from point A to point C.
Reason: Two points determine exactly one line.
3. <1 and <3 are congruent.
Reason: Alternate angles are congruent.
4. AC bisects angle <1 and angle <2.
Reason: Definition of angle bisector.
5. Measure of angle DAB is equal to the measure of angle BCD.
Reason: Opposite angles in a parallelogram are equal.
6. <2 and <3 are congruent.
Reason: Transitive property.
7. AB is equal to BC.
Reason: Sides opposite to congruent angles in a parallelogram are congruent.
8. <1 and <2 are congruent.
Reason: Corresponding parts of congruent angles are equal.
9. AB is equal to BC which is equal to CD which is equal to DA.
Reason: All sides of a rhombus are congruent.
Therefore, based on the given information and the steps of the proof, we can conclude that ABCD is a rhombus.
given rhombus ABCD, with diagonal BD and m<ABD=40,what is the m<A?
a=2/5
b= 2/3
d= 6/5