Answer:
To Prove: Quadrilateral ABCD is a parallelogram.
Proof: In Δ ABE and ΔCDE
1. AE = EC and BE = ED [ Diagonals bisect each other]
2.∠ AEB = ∠ CED [ vertically opposite angles]
Δ ABE ≅ ΔCDE---------- [SAS]
∠ ACD ≅ ∠CAB [Corresponding angles of congruent triangles are congruent⇒This statement is untrue ∴ these are alternate interior angles not corresponding angles.]
6. The converse of alternate interior interior angle theorem states that if two parallel lines are cut by a transversal then alternate interior angles are equal.
7. In ΔBEC and ΔAED
∠BEC = ∠AED [ Vertical Angles Theorem ]
AE = EC and BE = ED [ Diagonals bisect each other]
⇒ ΔBEC≅ ΔDEA [ SAS criterion for congruence]
9. DBC ≅ BDA [ Corresponding angles of congruent triangles are congruent⇒This statement is untrue ∴ these are alternate interior angles not corresponding angles.]
As pair of triangles are congruent ∵ quadrilateral ABCD is a parallelogram.
Step 3 is m∠AEB = m∠CED
These pair of angles are vertically opposite angles of ΔAEB and ΔCED.
Option [D. Vertical Angles Theorem] is correct.
Answer:
a) 6
Step-by-step explanation:
Expanding the polynomial using the formula:
Also
I think you mean
We can deduce that this term will be located somewhere in the middle. So I will calculate .
For
Note that we actually don't need to do all this process. There's no necessity to calculate the binomial, just
For
Answer:
The test contains 10 three-point questions and 14 five-point questions.
Step-by-step explanation:
The value of x is the number of 3-point questions, and the value of y is the number of 5-point questions, as the problem statement tells you. So, the solution (x, y) = (10, 14) indicates ...
"The test contains 10 three-point questions and 14 five-point questions."
_____
You can try the offered answers to see which might apply. The last choice has too many questions. The first and third choices don't add up to 100 points.
Answer:
Option "3" is the correct answer to the following question:
Step-by-step explanation:
Given:
Radius of cone (r) = 6 centimeter
height of cone (h) = 8 centimeter
slant height of cone (l) = 10 centimeter
Find:
Lateral surface area of the cone = ?
Computation:
⇒ Lateral surface area of the cone = rl
⇒ Lateral surface area of the cone = (6 centimeters) (10 centimeters)
⇒ Therefore, option "3" is the correct answer.