ABCD is a parallelogram with diagonals AC and BC intersecting O Prove that triangle AOB is congruent to triangle DOC
1 answer:
Given: ABCD is a parallelogram with diagonals AC and BD intersecting at O.
To prove: ∆AOB ≅ ∆DOC
Proof: Since ABCD is a parallelogram.
Therefore, AB || CD and AB = CD, AD || BC and AD = BC
Now, AB || CD and transversal AC intersects them a A and C respectively.
Therefore, Angle BAC = Angle DCA [Since alternate interior angles are equal]
or, Angle BAO = Angle DCO
Now, in ∆AOB and ∆DOC,
Angle BAO = Angle DCO [proved above]
AB = CD [opposite sides of a parallelogram are equal]
Angle AOB = Angle COD [vertically opposite angles are equal]
So, by ASA congruency,
∆AOB ≅ ∆DOC.
You might be interested in
The two-sided alternative hypothesis is appropriate in this case, the reason being we are asked "does the data indicate that the average body temperature for healthy humans is different from 98.6◦........?".
The test statistic is:
Using an inverse normal table, and halving
for a two-tailed test, we look up 
and find the critical value to be Z = 2.5758.
Comparing the test statistic Z = -5.47 with the rejection region Z < -2.5758 and Z > 2.5758. we find the test statistic lies in the rejection region. Therefore the evidence does not indicate that the average body temperature for healthy humans is different from 98.6◦.
The test statistic is:
Using an inverse normal table, and halving
Comparing the test statistic Z = -5.47 with the rejection region Z < -2.5758 and Z > 2.5758. we find the test statistic lies in the rejection region. Therefore the evidence does not indicate that the average body temperature for healthy humans is different from 98.6◦.