Mathematics
16.04.2023 02:44
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Look at the quadrilateral shown below: a quadrilateral abcd is shown with diagonals

Look at the quadrilateral shown below: a quadrilateral abcd is shown with diagonals ac and bd intersecting in point o. angle aob is labeled as 1, angle boc is labeled as 4, angle cod is labeled as 2, and angle aod is labeled as 3. clara writes the following proof for the theorem: if the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram: clara's proof 1. for triangles aob and cod, 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 cod are congruent by sas postulate. 4. similarly, triangles aod and cob are congruent. 5. by angle abd is equal to angle cdb and angle adb is equal to angle cbd. 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 missing phrase in clara's proof?
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jackiesantos1298
jackiesantos1298
5,0(9 marks)

answer: the missing part is cpct.

explanation:

here, we have, a quadrilateral abcd.

in which, diagonals ac and bd are bisecting each other. and, o is the point of intersection of line segments ac and bd. and, angle aob is labeled as 1, angle boc is labeled as 4, angle cod is labeled as 2 and angle aod is labeled as 3.

proof : abcd is a parallelogram.

now,   for triangles aob and cod,

angle 1 = angle 2 (because, they are vertical angles)

ao=oc and bo=od (because , it is given that diagonals bisect each other. )

\triangle aob\cong \triangle cod (by sas postulate)

similarly, triangles aod and cob are congruent.

by cpct("corresponding parts of congruent triangles are congruent"), m\angle abd=m\angle cd b

and, m\angle ad b=\angle cbd

as the alternate interior angles are congruent the opposite sides of quadrilateral abcd are parallel,

therefore, abcd is a parallelogram.

liliaboop2012
liliaboop2012
4,9(38 marks)
He pay $0.02 for each lollipop !

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