Match the following reasons with the statements given. Complete the proof for the theorem 4-18 mentioned above. 1. DO = OB, AO =
OC If two sides = and ||, then a parallelogram. 2. DOC = AOB Vertical angles are equal. 3. Triangle COD congruent to Triangle AOB CPCTE 4. 1 = 2, AB = DC Given 5. AB||DC If alternate interior angles =, then lines parallel. 6. ABCD is a parallelogram SAS
1 answer:
Answer: Please see attachment.
Solution:
We need to match the column using column proof. Please see the attachment for matching column.
In ΔDOC and ΔBOA
DO=BO (Given)
∠DOC=∠BOA (Vertically Opposite angle)
OC=OA (Given)
∴ ΔDOC ≅ ΔBOA by SAS congruence property
∠1=∠2 and AB=DC By CPCTE
Thus, AB||DC (∠1 and ∠2 are alternate angles equal then lines parallel)
ABCD is a parallelogram. ( If two sides equal and parallel then a parallelogram.
Below is matched table.
DO = OB, AO = OC ⇒ Given
∠ DOC =∠ AOB ⇒ Vertical angles are equal
∆COD ≅ ∆AOB ⇒ SAS CPCTE
∠1 = ∠2, AB = DC ⇒ CPCTE
AB||DC ⇒ If alternate interior angles =, then lines parallel
ABCD is a parallelogram ⇒ If two sides = and ||, then a parallelogram
Please see attachment for figure and matching.
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Answer:
The point is .
Step-by-step explanation:
Given:
The set of equations are:
Multiply equation 1 by 2, we get
----- 4
Add equations 3 and 4.
So, we got a new equation as -------- 5
Now, we multiply equation 1 by 3, we get
Now, add the following equations:
This gives,
We got another new equation as ------- 6
Now, we multiply equation 6 by -5, we get
Now, we add the above equation and equation 5:
Now, we plug in in equation 6, we get
Now, we plug in in equation 1, we get
Therefore,
The point is