Clara writes the following proof for the theorem, ñif the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram.î
claraís proof
1. for triangles aob and doc, angle 1 is equal to angle 2 as they are vertical angles.
2. ao = oc and bo = od because it is given that diagonals bisect each other.
3. the triangles aob and doc are congruent by sas postulate.
4. similarly, triangles aod and boc are congruent.
5. by transitive property, angle abd is equal to angle bdc and angle adb is equal to angle dbc.
6. as the alternate interior angles are congruent the opposite sides of quadrilateral abcd are parallel.
7. therefore, abcd is a parallelogram.
which is the first incorrect statement in clara’s proof?
answer
statement 4
statement 5
statement 6
statement 7

explanation:

clara's proof is as follows

1. ∠aob=∠cod→→→vertically opposite angles

2. oa=oc and ob=od→→{it is given that diagonals of quadrilateral bisect each other.]

3. δaob ≅δcod→→[sas]

4. similarly, δaod ≅ δboc →→[sas]

5. (a).∠abd=∠bdc, (b). ∠adb=∠dbc[cpct]

6. since the alternate interior angles are equal, or congruent the opposite sides of quadrilateral abcd are parallel.

7. as, if in a quadrilateral , opposite sides are parallel, and diagonals bisect each other , so it is a parallelogram.

the incorrect statement is :

statement 5. by transitive property, angle abd is equal to angle bdc and angle adb is equal to angle dbc. it shouldn't be transitive property , it should be cpct, that is corresponding parts of congruent triangles.

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.